f(x)=(x+3), h(x)=(3x-5)

Find g(f(x))=h

Basically its x+3=3x-5 so subtract x from 3 which gives u 2x then add 5 to the other 3 to balance it out which leaves u 2x=8. Divide each side by 2 and ur g is 4

let g(x) = ax + b

then
g(f(x))
= g(x+3)
= a(x+3) + b
= ax + 3a + b

but we know that
g(f(x)) = 3x - 5
so a = 3 and
3a+b = -5
9+b = -5
b = -14

then g(x) = 3x - 14

check:
g(f(x)) = 3(x+3) - 14
= 3x + 9 - 14
= 3x - 5 = h(x) !!

To find the expression g(f(x)) equal to h(x), we need to first substitute the equation f(x) = (x + 3) into the function g(x).

Let's proceed step by step:

1. Replace x in g(x) with the expression f(x) = (x + 3):
g(f(x)) = g(x + 3)

2. Substitute g(f(x)) with h(x) = (3x - 5):
h(x) = g(x + 3)

We have now reduced the problem to finding the function g(x) such that g(x + 3) = (3x - 5).

Since there is no given information about the function g(x), we cannot solve for the exact expression of g(x). However, if you provide an additional equation or information related to g(x), we might be able to find its specific expression.