Question

Consider the function and its inverse:
f(x)=1/3x-2

f^-1(x)=a(x+2)



The slope, a, of the inverse function is
, and the x-intercept of the inverse function is at x =
.

Answer 1

Slope a = 3.

To see this, solve y = (1/3)x − 2 for x: x = 3(y + 2), so f⁻¹(x) = 3(x + 2) and a = 3.
Set f⁻¹(x) = 0: 3(x + 2) = 0 → x = −2.