Question

Consider the function.



Which conclusions can be drawn about f–1(x)? Select two options.
f(x)=-2/3x-24
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.

Answer 1

First find the inverse. y = (-2/3)x - 24 → swap x,y: x = (-2/3)y - 24 → y = (-3/2)x - 36. So f⁻¹(x) = (-3/2)x - 36.

Therefore the true conclusions are:
- f⁻¹(x) has a y-intercept of (0, −36).
- f⁻¹(x) has a range of all real numbers.

(For reference: the slope of f⁻¹ is −3/2, and its domain is all real numbers — it is not restricted.)