Question

Please help me
Which of the following is the inverse of the function given below?

Answer 1

Option A.

Explanation:

The given function is

`f(x)=(x+2)/(7)`

Step 1: Substitute f(x)=y.

`y=(x+2)/(7)`

Step 2: Interchange x and y.

`x=(y+2)/(7)`

Step 3: Isolate y.

`7x=y+2`

`7x-2=y`

Step 4: Substitute
`y=f^(-1)(x)`

`7x-2=f^(-1)(x)`

`f^(-1)(x)=7x-2`

The inverse of the given function is
`p=7x-2`.

Therefore, the correct option is A.

Answer 2

The function is described by the rule
`f(x)= (x+2)/(7)`.

The inverse function
`f^(-1)` is such that
`f(f^(-1)(x))=x`.

Thus, since
`f(x)= (x+2)/(7)`, we have
`f(f^(-1)(x))=(f^(-1)(x)+2)/(7)`.

Equating the two ways we expressed
`f(f^(-1)(x))`, we have:


`\displaystyle{ (f^(-1)(x)+2)/(7)=x`.

Rearranging, we have:



`\displaystyle{ f^(-1)(x)= 7x-2`.



Answer: first choice: p(x)=7x-2