Question

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

Answer 1

Answer:

f^-1 (x) = ±sqrt(x-16)

Step-by-step 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)

Answer 2

Answer:

$y = \sqrt{x - 16}$

Step-by-step explanation:

$y = {x}^{2} + 16$

$x = {y}^{2} + 16$

$x - 16 = {y}^{2}$

$\sqrt{x - 16} = y$