Question

Find the inverse function.f(x) = 1/2 x + 1/2f-¹(x) = [? ]x+ []

Answer 1

`f(x)=(1)/(2)x+(1)/(2)`

To get the inverse, we first put y = f(x) then make x the subject, we have

`\begin{gathered} f(x)=(1)/(2)x+(1)/(2) \\ y=(1)/(2)x+(1)/(2) \\ y-(1)/(2)=(1)/(2)x \end{gathered}`

To remove the half fraction, multiply both sides of the equation by 2

`\begin{gathered} 2y-2((1)/(2))=2((1)/(2)x) \\ 2y-1=x \\ x=2y-1 \end{gathered}`

Now replace y with x and x with f(x) inverse, we have

`f^(-1)(x)=2x-1`

Hence the answer is

`f^(-1)(x)=2x+(-1)`