# Thread: [SOLVED] Find the domain of the composite function

1. ## [SOLVED] Find the domain of the composite function

Instructions: Find the domain of the composite function f (of) g.

f(x)= (-45)/(x) g(x)=(-7)/(x-9)

2. ## And Another Composite Function...

Here's another one.

Instructions: For the given functions f and g, find the requested composite function.

find (g (of) f) (x)

f(x)=(x-10)/(7) g(x)=7x+10

Here's what I got...I basically just want to check my answer:

g(f(x))= 7((x-10)/(7))+10

g(f(x))=x-10+10

g(f(x))=x

3. Originally Posted by GeminiAngel619
Instructions: Find the domain of the composite function f (of) g.

f(x)= (-45)/(x) g(x)=(-7)/(x-9)
You can study some online lessons to learn how to get started on finding the domain of a function.

Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.

(Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)

Originally Posted by GeminiAngel619
Instructions: For the given functions f and g, find the requested composite function.

find (g (of) f) (x)

f(x)=(x-10)/(7) g(x)=7x+10

Here's what I got...I basically just want to check my answer:

g(f(x))= 7((x-10)/(7))+10

g(f(x))=x-10+10

g(f(x))=x
Your work looks good to me!

4. Originally Posted by stapel
You can study some online lessons to learn how to get started on finding the domain of a function.

Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.

(Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)

Your work looks good to me!
Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.

Here's how I got -7=0:

(-7)/(x-9)=0

multiply both sides by common denom. (x-9)

and you get (-7)=0.

This is where I'm stuck.

5. ## So in other words...

The restrictions on the domain are x cannot equal 9 or 0. I understand that part. Its the next step that I'm not doing so hot on. lol

6. Originally Posted by GeminiAngel619
Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.
What does that tell you? Can $g(x)$ ever be zero? Think about it.

find (g (of) f) (x)

f(x)=(x-10)/(7) g(x)=7x+10

Here's what I got...I basically just want to check my answer:

g(f(x))= 7((x-10)/(7))+10

g(f(x))=x-10+10

g(f(x))=x
Correct. You would get the same thing with $(f\circ g)(x)$ (but that doesn't always happen). We say that $f$ and $g$ are inverses of each other, because they "undo" each other, so to speak.