Question

I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2

Answer 1

`f(x)=\frac{x^2-4^{}}{2x^2}`

to solve this problem, we can follow some steps

step 1

replace f(x) with y

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

step 2

replace every x with a y and every y with an x

`\begin{gathered} x=(y^2-4)/(2y^2) \\ \end{gathered}`

step 3

solve for y

`\begin{gathered} x=(y^2-4)/(2y^2) \\ \text{cross multiply both sides} \\ 2y^2* x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ (y^2(2x-1))/((2x-1))=-(4)/((2x-1)) \\ y^2=-(4)/(2x-1) \\ \text{take the square root of both sides} \\ y=-\sqrt[]{(4)/(2x-1)} \end{gathered}`

therefore the inverse of f(x) is

`f^(-1)(x)=-\sqrt[]{(4)/(2x-1)}`