Question

What equation is the inverse of y=x^2+16

Answer 1

`y = √(x - 16)`

Explanation:

`y = {x}^(2) + 16`

`x = {y}^(2) + 16`

`x - 16 = {y}^(2)`

`√(x - 16) = y`

Answer 2

f^-1 (x) = ±sqrt(x-16)

Explanation:

To find the inverse of a function, exchange x and y and solve for y

y=x^2+16

Exchange x and y

x = y^2 +16

Then solve for y

Subtract 16 from each side

x-16 = y^2 +16-16

x-16 = y^2

Take the square root of each side

±sqrt(x-16) = sqrt(y^2)

±sqrt(x-16) = y

The inverse

f^-1 (x) = ±sqrt(x-16)