The functions given are f(x) = 1/(x - 2) and g(x) =
4/x.
(f*g)(x) = fog(x) =
f(g(x)).
To find f(g(x)), first we find g(x). g(x) =
4/x.
Substituting this in
f(x)
=>
f((4/x))
=> 1/ ((4/x) -
2)
=> 1 / [(4 -
2x)/x]
=> x / (4 -
2x)
Therefore the required result is x / (4 -
2x)
The main issue on Prufrock's mind is a deeply personal and
intimate one--he wants to ask someone that he cares about an "overwhelming question" of
serious import. That subject--whether to ask her, when, how, and what impact it might
have, and if he will be rejected-- is the subject that his mind keeps coming back to.
It is a personal, intimate subject, and the reader can feel that closeness. In the
meantime, however, his mind wanders. In the stream-of-consciousness style that Eliot
uses, he lets Prufrock's mind wander about as he ponders this issue. It reminds me of
someone sitting on a porch or a couch, thinking about what to do, but it's stressful, so
they kind-of avoid focusing too hard on the subject, and let their mind stray and wander
about to avoid thinking about it too much.
So, to
specifically answer your question, look at how the poem starts--it begins with a very
distant perspective, inviting the reader, or the person to whom he's speaking, to go for
a little walk through the run-down part of town. "Let us go then, you and I," he
invites, and the invitation is distant and impersonal as he describes the journey
through the "sawdust restaurants." He then uses a transition to bring it back to the
personal; he describes the streets that wind around town, which remind him of a "tedious
argument of insidious intent." This leads him right into the personal--he brings up
"the question." The streets are like an argument; this is stressful, and reminds him of
asking the question. That is personal. But he very quickly withdraws from that and
gets impersonal again by saying, "Let us go and make our visit." He's avoiding the
personal again, and distracting the reader.
He proceeds to
describe the fog, parties, inane conversations, etc. But each time, something in the
ramblings of his mind reminds him of the personal, and he comes back to it. It is in
this way that he transitions from the impersonal to the intimate. I hope that those
thoughts helped; good luck!
The question is a great one, but it does need a specific
poem. I think that there is much in Hughes' body of work that explores the pain of
being black in America. There is not much else to say on it because being a person of
color at the time of Hughes' writing did involve a great deal of pain. Yet, I think
it's important to note that what differentiates Hughes from other writers is that this
pain does not blight or dull a sense of resistance and almost collective solidarity to
strive to make things better. Unlike some of his colleagues in the pantheon of African
America literature like Dunbar or Cullen, Hughes is very passionate about the idea that
while there is pain in the Black experience in America, there is also a reservoir of
collective strength from which drawing can help make what is difficult something that
represents a source of greatness, a source of inspiration for others. For example, in
the poem, "I, Too," there is pain at being humiliated, but a source of personal strength
that sees one's contextual struggle in a larger scope and sequence. In "The Negro
Speaks of Rivers," one sees the wide historical presence Black people have held in world
history, contributing to the understand that what is endured now is part of a larger
dynamic. In "Theme for English B," there is a certain amount of pain about what the
speaker's existence is lacks connection to the teacher's or the colleagues', but there
is a validation of voice present that acknowledges and accepts what is into being what
should be. In this light, Hughes' work does throw light on the pain of being black, but
does so in a manner to ensure that this is not the only condition that being black
contains.
Water is composed of two hydrogen atoms covalently bonded
to a single oxygen atom. Each hydrogen atom shares a pair of electrons with the oxygen
atom, resulting in a slight positive charge on the hydrogen atoms and a slight negative
charge on the oxygen atom, otherwise known as a "dipole moment" or polar charge.
Normally, the molecule would have tetrahedral geometry with 109.5 degrees between
atoms, but the molecule actually has a non-linear geometry because the negative charges
try to minimize their overlap, and the angle is reduced slightly to 104.5
degrees.
Song is describing a print of a scene where a woman is
putting on makeup and grooming herself. The fact that he is looking at a picture is
important because it is a moment frozen in time. The poem is about the transitory nature
of beauty, the objectification of women and what women go through to sustain beauty. The
picture freezes this moment. In reality, beauty does not last. The line “she is about to
paint herself” literally illustrates that she is creating beauty. It is fake. It is a
mask she must routinely reapply because that is the role she’s been
given.
Morning
begins the ritualwheel of the
body,the application of translucent
skins.She practices pleasure:
(16-19)
She is a courtesan.
This could mean she is someone who attends court, pays close attention to some authority
figure, or it could also mean she is a prostitute. In the case of the latter, not only
is her beauty transitory and for show; it is also for sale. The woman is confined to
this position in life. Her inner self is hidden under these layers of beauty (powder and
makeup). She is selling her own objectification. Her beauty is all that matters to those
around her. They do not care about her mind.
The mouth parts
as
if desiring to disturb
the placid plumb
face;
break the symmetry of
silence.
But the berry-stained
lips,
stenciled into the mask of
beauty,
do not speak.
(43-49)
Her voice and
personality are confined by the “mask of beauty.” She must live in a society where she
is admired for her beauty; not her intellect. Therefore, she is forced to continue the
ritual to keep up the appearance of being beautiful. Otherwise, she will become
irrelevant. Her “placid plumb face” and “berry-stained lips” are a painting. This image
is dead; just like the picture itself. She has become a picture; not a person. A picture
cannot speak.
In Chapter 8 of The Autobiography of Malcolm
X, Billie Holliday is also known as "Lady Day." Look on page 132 to find the
answer.
Malcolm describes how she would come over to his
table at the Onyx Club. On the night Malcolm had it out with West Indian Archie, "Lady
Day" came over to his table to ask what was wrong. Malcolm says she knew he was always
high, and on this night, she thought he looked
worried:
...she knew me well enough to see something else
was wrong, and asked in her customary profane language what was the matter with
me.
Malcolm then describes
her death, which happened years later. It was drug
related:
That
was the last time I ever saw Lady Day. She's dead; dope and heartbreak stopped that
heart as big as a barn and that sound and style that no one successfully copies. Lady
Day sang with the soul of Negroes from the centuries of sorrow and
oppression.
Macduff goes with Malcolm to England to get military
support to reclaim the throne from Macbeth. Lennox does not believe Duncan was murdered
by his sons and clearly, Macduff is thinking the same thing. I don’t think it is clear
that Macduff realizes the implications of his not attending Macbeth’s banquet. It is
clear that Macbeth takes this rebuff as Macduff opposing his right to the throne. Also,
Macduff cannot know what the weird sisters have said to Macbeth (the first apparition
says beware Macduff); so Macduff can’t know just how seriously Macbeth sees him as a
threat. Still, I can see how it makes much more sense for Macduff to take his family
with him. But I think this is something he could only see in hindsight. Also, no one
except Lady Macbeth was privy to Macbeth’s growing insecurities and madness and so no
one but her (sans the weird sisters/witches) could foresee Macbeth’s subsequent killing
spree.
