14
QuizMultiple Choice

Exponential and Logarithmic Functions — Test

Question 14 • Algebraic Reasoning

Consider the function. f of x is equal to negative 2 thirds x minus 24 Which conclusions can be drawn about f inverse of x ? Choose two correct answers.

Answer
A
f inverse of x has a range of all real numbers.
B
f inverse of x has a y - intercept of open paren 0 comma negative 36 close paren .
C
f inverse of x has a restricted domain.
D
f inverse of x has a slope of negative 2 thirds .
E
f inverse of x has an x - intercept of open paren negative 36 comma 0 close paren .

Explanation

To find the inverse, interchange x and y in y = -(2/3)x - 24 and solve for y. This gives f⁻¹(x) = -(3/2)x - 36, so its y-intercept is (0, -36), as stated in choice B. Because this inverse is a nonconstant linear function, its range is all real numbers, as stated in choice A.

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