Question

If g :R → R is given by g(x) = x2 + 3 , find the function f such that (g. f) (x) = 4x2 + 3. A. 3x B. 4x C. 2x D. None of these

Answer 1

Given:

`\begin{gathered} g(x)=x^2+3_{} \\ (g\circ f)(x)=4x^2+3 \end{gathered}`
`(g\circ f)(x)=g(f(x)`

Let substitute one by one from the given options.

`\begin{gathered} g(3x)=(3x)^2+3 \\ g(3x)=9x^2+3 \end{gathered}`

3x is not the function f.

`\begin{gathered} g(4x)=(4x)^2+3 \\ g(4x)=16x^2+3 \end{gathered}`

4x is not the function f.

`\begin{gathered} g(2x)=(2x)^2+3 \\ g(2x)=4x^2+3 \end{gathered}`

2x is the function f.

`f(x)=2x`

Option C is the final answer.