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

Answer:

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

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

Step-by-step explanation:

Given the function: $f(x)= -\dfrac23x-24$

$f(x)+24= -\dfrac23x\\ Multiply both sides by -\dfrac32\\x=-\dfrac32(f(x)+24)\\f^{-1}(x)=-\dfrac32f(x)-36$

When y=f(x)=0

$f^{-1}(x)=-\dfrac32(0)-36\\f^{-1}(x)=-36$

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.