Given f(x) = sin(x) , g(x) = 1/x , h(x) = |x|, state h(g(f(x)))?

Given f(x) = sin(x) , g(x) = 1/x , h(x) = |x|, state h(g(f(x)))?

So I'm able to do the first two steps
f(g(sinx))
f(1/sin)

But I'm not sure what the last step does. Normally something enclosed inside ||, such as |x| means the magnitude of x, right? So what does that operator mean in the context of this problem? How does y=1/sinx differ from y=|1/sinx|? Obviously, this can be written as y=|csc|.

b) Describe what each composition does in the order that it is applied. Again, I'm fine until the last function, where I don't know what the operator does.

c) sketch the curve. My curve looks like a csc function, is this correct? Please help

Quote:

---

Originally Posted by stacey

Given f(x) = sin(x) , g(x) = 1/x , h(x) = |x|, state h(g(f(x)))?

So I'm able to do the first two steps
f(g(sinx))
f(1/sin)

But I'm not sure what the last step does. Normally something enclosed inside ||, such as |x| means the magnitude of x, right? So what does that operator mean in the context of this problem? How does y=1/sinx differ from y=|1/sinx|? Obviously, this can be written as y=|csc|.

b) Describe what each composition does in the order that it is applied. Again, I'm fine until the last function, where I don't know what the operator does.

c) sketch the curve. My curve looks like a csc function, is this correct? Please help

---

h(g(f(x)))=h(g(sin(x)))=h(1/sin(x))=|1/sin(x)|=1/|sin(x)|=|cosec(x)|

There is a difference between cosec(x) and |cosex(x)|.

Start by drawing y=cosec(x) and try to understand what the operation | | doing to cosec(x).

(Maybe you should draw the function f(x)=x tnd afterwards to draw g(x)=|x|, it will give you a clue)

Quote:

---

Given f(x) = sin(x) , g(x) = 1/x , h(x) = |x|, state h(g(f(x)))?

---

Let's start with the inside, and work our way out. g(f(x)) is the same as g(sin(x)), which is the same as 1/sin(x). Our final result is then h(1/sin(x)). When you subsitute the x in |x| with 1/sin(x), what do you get?

Hello, stacey!

Quote:

---

But I'm not sure what the last step does.
Normally something enclosed inside ||, such as |x| means the magnitude of x, right?
So what does that operator mean in the context of this problem?
How does differ from ?
Obviously, this can be written as . Yes!

b) Describe what each composition does in the order that it is applied.
Again, I'm fine until the last function, where I don't know what the operator does.

---

Evidently, you're not familiar with "absolute values".
(I'm not sure how that happened to you.)

means: take the positive value of

. .

When graphing, any portion below the x-axis is reflected upward above the x-axis.

Quote:

---

c) sketch the curve.
My curve looks like a csc function. .Is this correct?

---

Not quite . . . It is the cosecant graph, but everything is "made positive".

It looks something like this:

. .