Question

F(x) = 3x-1 , (f of g)(x) = x^2 , Find g(x)

Answer 1

Answer:

$g(x)=\dfrac{x^2+1}{3}$

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}$

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).

$\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}$

Therefore:

$\boxed{g(x)=\dfrac{x^2+1}{3}}$