Question

Find the inverse of g(x) = x^2 - 9. Determine whether the inverse is a function.

Answer 1

a) not a function
\[y= \pm \sqrt{x+9}\]
b) function
\[y= \pm \sqrt{x+9}\]
c) not a function
\[ y= \pm \sqrt{x}+9\]
d) function
\[ y= \pm \sqrt{x}+9\]

Answer 2

not likely for the inverse to be a function since \(x^2-9\) is not "one to one"

Answer 3

for example \(f(4)=16-9=7\) and also \(f(-4)=16-9=7\)

Answer 4

to find the inverse, set \(x=y^2-9\) and solve for \(y\) in two steps

Answer 5

\[y=\sqrt{x}+9\]
and its a function