Question

х = X 1 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

C. 2x

Step-by-step explanation

The composition (g o f)(x) is,

`(g\circ f)(x)=g(f(x))`

So, if g(x) = x² + 3, replace x with f(x),

`(g\circ f)(x)=f(x)^2+3=4x^2+3`

Solve for f(x). Subtract 3 from both sides,

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

And take a square root,

`f(x)=2x`

Hence, the function f(x) is 2x