How do you find the compositions given $g(x) = x^2 + 2$ and $f(x) = 2x$ ?

Question

1219 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-20T18:43:17

Compose the functions to find that

$(f@g)(x) = 2x^2$
and
$(g@f)(x) = 4x^2$

Composing functions is a simple as treating a function like a variable.

For $f(x) = 2x$ and $g(x) = x^2$ we have

$(f@g)(x) = f(g(x)) = f(x^2) = 2(x^2) = 2x^2$

and

$(g@f)(x) = g(f(x)) = g(2x) = (2x)^2 = 4x^2$

How do you find the compositions given g(x) = x^2 + 2g(x) = x^2 + 2 and f(x) = 2xf(x) = 2x?