1.) If h(x)= (fog)(x) and h(x) = 3 over the square root of x+3 , find g(x) if f(x)= 3 over the square root of x+2.

Question

my answer is x+1. Am I right?

2.)If f(x)=3x,g(x)=x-3,and h(x)= the square root of x, find (fogox)(X). I really didn't get this will someone please show me how to do it?

Answer 1

The first one is correct but I am still not sure about the second one.
This I what I did to solve for it:
3(x-3)
3(he square root of 25-3
3(5-3)
15-9=6

Is it correct?

Answer 2

f(x) = 3/√(x+2)
f(g) = 3/√(g+2) = 3/√(x+3)
so, you are correct; g(x) = x+1

for the second one, you're not solving any equation; you're just expressing a composite function as a single one, just as in #1.

f(x) = 3x
g(x) = x-3
h(x) = √x

(f◦g◦h)(x) = f(g(h(x)))
f(g(h)) = f(h-3) = 3(h-3) = 3(√x-3)
or,
f(g(h)) = 3(g(h)) = 3(g(√x)) = 3(√x-3)