Question

F (x) = -3 + 7. Find the inverse of f(x) and its domain.

O A. f-1(x) 277 - 3, where x=-7
O B. f-1(x) = +7 +3, where x# 7
c. f-1(x) = 11 – 3, where x# 3
O D. f-1(x) = + 3, where x# 3
S

Answer 1

Note: Your function is missing some information. It seems your function is

`f\left(x\right)=(-3)/(x)+7`.

So, I am solving the question based on the function
`f\left(x\right)=(-3)/(x)+7`, because it would still solve your query.

Answer:

Please see the explanation.

Explanation:

Given the function

`f\left(x\right)=(-3)/(x)+7`

A function g is the inverse of a function f for y = f(x), x=g(y)

`y=(-3)/(x)+7`

Replace x with y

`x=(-3)/(y)+7`

solve for y

`y=-(3)/(x-7)`

so the inverse of
`f\left(x\right)=(-3)/(x)+7` will be:

`f^(-1)\:\left(x\right)=-(3)/(x-7)`

Finding the domain of
`f^(-1)\:\left(x\right)=-(3)/(x-7)`

As we know that domain is the set of the possible input values where the function is defined.

so the function domain must be:
`x<7\quad \mathrm{or}\quad \:x>7`

Therefore,

`\mathrm{Domain\:of\:}\:-(3)/(x-7)\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<7\quad \mathrm{or}\quad \:x>7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:7\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}`