Question

Given f(x)=-1/7√16-x^2 find f^-1(x)

Answer 1

f^-1(x)= + or - square root 49x^2-16

Explanation:

edge 2020 2021

Answer 2

`f^(-1)(x)=\pm √(49x^2-16)`

Not a function.

Explanation:

The given function is;

`f(x)=-(1)/(7)√(16-x^2)`

Let
`y=-(1)/(7)√(16-x^2)`

Interchange x and y;

`x=-(1)/(7)√(16-y^2)`

Solve for y;

`-7x=√(16-y^2)`

Square both sides

`(-7x)^2=(√(16-y^2))^2`

`49x^2^2=16-y^2`

`49x^2^2-16=y^2`

`y=\pm √(49x^2-16)`

The inverse is

`f^(-1)(x)=\pm √(49x^2-16)`

`f^(-1)(x)=\pm √(49x^2-16)` is not a function because one x-value maps onto to different y-values.