Let g (x)=2 x^2-4,if(f o g)(x)=2x-4,

Question

find f(x)?

 

 

Answer 1

The functions are .

Find f(x) as follows :

Let and find its inverse function.

Replace h(x) with y.

Interchange x and y.

Add 4 to each side.

Divide each side by 2.

Replace y with h^{- 1}(x) and consider only positive value because to find the solution.

Multiply each side by 2.

Subtract 4 from each side.

Let

Check : .

The function .