Question

Use the functions to answer the question.
f(x)=3x; g(x)= 4x^2=1
which is equal to (fog)(x)?
please explain i dont get this at all

Answer 1

This is a composition of functions. We take what g(x) equals for any value (we'll call that value "x") and plug what g(x) equals as the input into f(x). In other words, the input (a.k.a. x) for f(x) will be g(x).

\[g(x)=4x^2-1\]
So we need to find \[(f\dot{}g)(x) = f(g(x)) = f(4x^2-1)=3(4x^2-1)=12x^2-3\]
We take the result of g(x) and plug it in as x for f(x), which is equal to 3x. So basically, whatever g(x) gives, when we put it into f(x), it will be multiplied by 3. So again, the answer is:
\[(f\dot{}g)(x)=12x^2-3\]

Answer 2

Thank you