Question

Which function is the inverse of f(x)=x^2-25

Answer 1

To find the inverse of a function, firt we let

$f(x) = y= x^2-25$

Now we switch x and y and solve for y .

$x = y^2 -25$

Adding 25 to both sides

$x+25 = y^2$

Now we need to get rid of square and for that we take square root on both sides. That is

$y = +- \sqrt{x^2 +25}$

Therefore, inverse is

$f^{-1}(x) = - \sqrt{x^2 +25} , \sqrt{x^2 +25}$

Answer 2

f(x) = x² -25

Step 1:

write f(x) as y

y=x² -25

Step 2:

switch x as y and y as x

x=y²-25

Step 3:

solve for y

x=y²-25

add 25 to the left side

x+25 = y²

taking square root on both sides

y=√(x+25)

f⁻⁻¹(x) =√(x+25)