function composition

Question

i need help finding and simplifying

1. F(g(x))
2. G(f(x))
3. F(g(0))

If f(x) = 3x – 1 and g(x) = 2 – 5x

Answer 1

When you are given f(1), you plug in "1" for "x" in the function f(x). If you are given f(7), you plug in "7" into f(x). If you are given f(g(x)) then you plug in the function g(x) into the function f(x) wherever there is an "x".

So since f(x) = 3x -1 then f(g(x)) is 3(2 - 5x) - 1. Instead of writing "x" in f(x", I wrote "2 - 5x" which is g(x).

So now, just simplify:

f(g(x)) = 3(2 - 5x) - 1

f(g(x)) = 6 - 15x -1

f(g(x)) = 5 - 15x

For g(f(x)), plug in the function f(x) into the function g(x) wherever there is an "x" so since g(x) = 2 - 5x, then g(f(x)) = 2 - 5(3x – 1)

g(f(x)) = 2 - 15x + 5

g(f(x)) = 7 - 15x

For f(g(0)) you can either plug zero into the f(g(x)) we got in the first problem, so f(g(0)) = 5 - 15(0) = 5 OR you can plug zero into g(x) to get 2 - 5(0) = 2 then take the 2 and plug it into f(x) to get 3(2) - 1 = 5