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)