Question

Select the correct answer.IWhat is the inverse of the function f(x) = +1²?IIOA.f(x)= I + 11OB. j-¹(x)=√ ² 1--OC. f(x)= I 1I + 1IOD. 1-²¹(x)=,=1I

Answer 1

The function is given below as

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

Concept:

we will substitute f(x)= y and make x the subject of the formula

`\begin{gathered} f(x)=(x+1)/(x) \\ y=(x+1)/(x) \\ cross\text{ multiply, we will have} \\ xy=x+1 \\ xy-x=1 \\ x(y-1)=1 \\ divide\text{ both sides by y-1} \\ (x(y-1))/(y-1)=(1)/(y-1) \\ x=(1)/(y-1) \\ replace\text{ y with x} \\ f^(-1)(x)=(1)/(x-1) \end{gathered}`

Hence,

The final answer is

`\Rightarrow f^(-1)(x)=(1)/(x-1)`

OPTION B is the right answer