Answer:
Yes. f(x) and g(x) are inverses of one another
Step-by-step explanation:
[tex]f(x) = - \frac{1}{2} x - 2 \\ y = - \frac{1}{2} x - 2 \\ x = - \frac{1}{2} y - 2 \\ x + 2 = - \frac{1}{2} y \\ - 2(x + 2) = - \frac{1}{2} y \times - 2 \\ - 2x - 4 = y \\ {f }^{ - 1} (x) = - 2x - 4[/tex]
In step 1 we just copied the original function.
In step 2 we substituted y for f(x).
in step 3 we switched the variables.
in step 4 we added 2 to both sides.
in step 5 we multiply both sides by -2
In step 6 we solved for y.
In step 7 is just a fancy way of saying the inverse function f(x) = -2x - 4
