Which function has an inverse that is also a function? g(x)=2x-3 k(x)=-9x^2 f(x)= |x+2| w(x)=-20

For each of these, we would solve for the inverse function and then do the vertical line test to check if it is a function:

g(x)=2x-3
g(x)+3=2x
x=(g(x)+3)/2
If you graph this inverse function and do the vertical line test, you see that it is a function.

k(x)=-9x²
k(x)/-9=x²
√-(k(x)/9)=x
This is not an equation because you can't take the square root of a negative number, so it is not a function.

f(x)=x+2 or f(x)=-(x+2)
x=f(x)-2  or f(x)=-x-2
                   x=-(f(x)+2)
If you graph this piecewise function, it does not pass the vertical line test, so the inverse is not a function.

w(x)=-20
Since this is a horizontal line, the inverse is a vertical line, which isn't a function.