Question

Let f(x) = x2 - 16. Find f-1(x)

Answer 1

To find the inverse of f(x):
1. Replace f(x) with y: y = x^2 - 16
2. Switch 'x' and 'y': x = y^2 - 16
3. Solve for y: x + 16 = y^2. y = sqrt(x+16).
4. Replace y with f-inverse or f^(-1)(x): f^(-1)(x) = sqrt(x+16)

Answer 2

I was thinking,

\(\large\color{slate}{ \displaystyle y=x^2-16}\)
\(\large\color{slate}{ \displaystyle 0=x^2+0x-(16-y)}\)

\(\large\color{slate}{ \displaystyle x=\frac{-(0)\pm\sqrt{0^2-4(1)(16-y)}}{2(1)} }\)

\(\large\color{slate}{ \displaystyle x=\frac{\pm\sqrt{4(1)(y-16)}}{2} }\)

\(\large\color{slate}{ \displaystyle x=\pm\sqrt{(y-16)} }\)

and in inverse you replace, so
\(\large\color{slate}{ \displaystyle f^{-1}(x)=\pm\sqrt{(x-16)} }\)

Answer 3

So I think the \(\large\color{slate}{ \displaystyle \pm }\) should be there.

Answer 4

\[
\large\color{slate}{ \displaystyle f^{-1}(x)=\pm\sqrt{(x+16)} }
\]