What's the inverse of y = 100 - x^2

The inverse is ±sqrt (100-x)

Step-by-step explanation:

y = 100 - x^2

Exchange x and y

x = 100 - y^2

Solve for y

Subtract 100 from each side

x-100 = 100-100-y^2

x-100 = - y^2

Multiply by - 1

-x+100 = y^2

100 - x = y^2

Take the square root of each side

±sqrt (100-x) = sqrt (y^2)

±sqrt (100-x) = y

The inverse is ±sqrt (100-x)

y = ±√ (100 - x)

Step-by-step explanation:

Given: y = 100 - x²

To find the inverse, we have to rearrange the equation such that we express x in terms of y.

y = 100 - x² (add x² to both sides)

y + x² = 100 (subtract y from both sides)

x² = 100 - y

x = ±√ (100 - y) (final step: swap x and y terms)

y = ±√ (100 - x) (answer)