Instructions: Find the domain of the composite function f (of) g.
f(x)= (-45)/(x) g(x)=(-7)/(x-9)
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
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.
What does that tell you? Can $\displaystyle g(x)$ ever be zero? Think about it.
Correct. You would get the same thing with $\displaystyle (f\circ g)(x)$ (but that doesn't always happen). We say that $\displaystyle f$ and $\displaystyle g$ are inverses of each other, because they "undo" each other, so to speak.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