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 -2/3 . 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

4 and 5

Explanation:

EDGE

Answer 2

(D)
`f^(-1){(x$) has an x-intercept of (-36, 0).`

(E)
`f^(-1){(x)` has a range of all real numbers.

Explanation:

Given the function:
`f(x)= -\frac23x-24`

`f(x)+24= -\frac23x\\$Multiply both sides by $ -\frac32\\x=-\frac32(f(x)+24)\\f^(-1)(x)=-\frac32f(x)-36`

When y=f(x)=0

`f^(-1)(x)=-\frac32(0)-36\\f^(-1)(x)=-36`

Therefore,
`f^(-1)(x)$ has a x-intercept of -36`

Also,
`f^(-1)(x)` has a range of all real numbers.

Therefore, Options D and E are correct.