Question

Which equation is the inverse of y=100-x2

Answer 1

Answer:

Inverse of y = $f^{-1}(x)$ = $\sqrt{100 -x}$.

Step-by-step explanation:

Given  : f(x) = y = 100 - x²

To find : Find inverse.

Solution : We have given that :

f(x) = y = 100 - x²

Step1) : Replace every x with a y and replace every y with an x .

x = 100 - y².

Step 2): Solve for y

On subtracting 100 from both sides

x - 100 = -y²

On multiplying both side by -1

100 -x = y²

Taking square root both sides and switching sides

y = ± $\sqrt{100-x}$.

Step3 ) : Replace y with $f^{-1}(x)$.

$f^{-1}(x)$ = ± $\sqrt{100-x}$.

Therefore, inverse of y = $f^{-1}(x)$ = ± $\sqrt{100-x}$.