Question

Let f(x)=-5x+1 and g(x)=-2x. Find the composition functions (fog)(x) and (gof)(x).

Can someone solve this step by step? I don't know how to do it..

Answer 1

Pay attention at notation:
\(f(\color{red}{x})=-5\color{red}{x}+1\)
If you don't have x, but g(x), then you just replace g(x) anywhere you see x, like
\(f(\color{red}{g(x)})=-5\color{red}{g(x)}+1\)
got me so far??

Answer 2

yeah so what next?

Answer 3

just replace g(x) = -2x from the right hand side, you will have
\(f(\color{red}{g(x)})=-5(\color{red}{-2x})+1\)
simplify the right hand side, use another notation from the left hand side, you have
\((fog)(x) = 10x+1\)
that's it

Answer 4

Imitate exactly for (gof)(x) , show me your stuff, please

Answer 5

oh ok thank you so much! It might take me a few

Answer 6

What do I replace x with? do I replace it with -5x+1?

Answer 7

Yup

Answer 8

ok so the same answer 10x+1?