Question

Consider the function.

f(x)=-2/3x -24

Which conclusions can be drawn about f–1(x)? Select two options.

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

Find the inverse: y = -2/3 x - 24. Swap x and y and solve for y:

x = -2/3 y - 24
x + 24 = -2/3 y
y = -3/2 (x + 24) = -3/2 x - 36

Thus f⁻¹(x) = -3/2 x - 36. So the two correct choices are:
- f⁻¹(x) has a slope of -3/2.
- f⁻¹(x) has a y-intercept of (0, –36).