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 ever be zero? Think about it.
Correct. You would get the same thing with (but that doesn't always happen). We say that and 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