Question

f(x)=2x^2+3 and g(x)=x^3
what is g(f(x))?

i know the answer is (2x^2+3)^3, but can someone explain the steps?

Answer 1

To find g(f(x)), you replace the x in the equation of g(x) with f(x)

We know
\( g(\color{red}{x})= \color{red}{x}^3\)

Then what is
\( g(\color{red}{f(x)}) = ??\)

Since they tell us f(x) = 2x^2 + 3

You just have to replace the red x with 2x^2 + 3
because that's what f(x) is equal to

That's how you get

\( g(\color{red}{f(x)}) = \color{red}{(2x^2+3)}^3\)