To find the inverse of a function, firt we let
[tex] f(x) = y= x^2-25 [/tex]
Now we switch x and y and solve for y .
[tex] x = y^2 -25 [/tex]
Adding 25 to both sides
[tex] x+25 = y^2 [/tex]
Now we need to get rid of square and for that we take square root on both sides. That is
[tex] y = +- \sqrt{x^2 +25} [/tex]
Therefore, inverse is
[tex] f^{-1}(x) = - \sqrt{x^2 +25} , \sqrt{x^2 +25} [/tex]
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)
