Question

Which function below is the inverse of f(x) = x2 − 25?

x squared over 25

±square root of the quantity x plus 25

±5 times the square root of x

1 over quantity x squared minus 25

Answer 1

\(f(x)=x^2-25\)

The first thing you have to do is put it in terms of x and y.

\(y=x^2-25\)

Then you flip the x and y.

\(x=y^2-25\)

Then you solve for y. Then replace y with f(x).
I am relatively sure that this is how you do it.

Answer 2

\(\bf f(x) ={\color{red}{ y}}= {\color{blue}{ x}}^2 - 25\qquad inverse\implies {\color{blue}{ x}}= {\color{red}{ y}}^2 - 25\)

solve for "y"

notice that to get the inverse "relation", we simply swap about the variables

Answer 3

replace y with \(f^{-1}(x)\)

Answer 4

thanks

Answer 5

No problemo! Have a great day.