Answer:
See below.
Step-by-step explanation:
[tex] f(x) = x^2 - 16 [/tex]
Replace f(x) with y.
[tex] y = x^2 - 16 [/tex]
Switch x and y.
[tex] x = y^2 - 16 [/tex]
Solve for y.
[tex] y^2 = x + 16 [/tex]
[tex] y = \pm\sqrt{x + 16} [/tex]
Replace y with f^(-1)(x).
[tex] f^{-1}(x) = \pm\sqrt{x + 16} [/tex]
The relation above is not a function, so the given function f(x) does not have an inverse unless the domain is restricted.
Answer:
F-1(x) = √(x + 16).
Step-by-step explanation:
Let y = x^2 - 16
First make x the subject:
x^2 = y + 16
x = √(y + 16)
Now replace x by the inverse f-1(x) and replace y by x:
f-1(x) = √(x + 16).
Note we only take the positive square root otherwise we would not have a function.
