Question

Consider the three functions: f(x) = Three-halves(4)x g(x) = Three-halves(4)–x h(x) = –Three-halves(4)x Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply. f(x) has a domain of all real numbers. g(x) has a range of y < 0. h(x) has a range of y > 0. g(x) has a domain of all real numbers. h(x) has a domain of x > 0.

Answer 1

The correct option is;

The ranges of f(x) and h(x) are similar and different from the ranges of g(x)

Explanation:

Here we have the functions given as follows;

f(x) = -6/11 (11/2)ˣ

g(x) = 6/11 (11/2)⁻ˣ

h(x) = -6/11 (11/2)⁻ˣ

from the above equations, it can be seen that f(x) and h(x) are always negative while g(x) is always positive

f(x) and h(x) are symmetric about the y axis while g(x) and h(x) are symmetric about the x axis

Also h(x) is the inverse of f(x) hence the ranges of f(x) and g(x) are similar and are different from the ranges of g(x).

Answer 2

A and D

Explanation:

A.) f(x) has a domain of all real numbers.

D.) g(x) has a domain of all real numbers.