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. g (x) has a domain of all real numbers. h (x) has a domain of x > 0.

Question

Mathematics

Tristen

25 December, 05:19

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. g (x) has a domain of all real numbers. h (x) has a domain of x > 0.

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Answers (2)

Know the Answer?

Demarion Buck · Answer 1

A and D

Step-by-step explanation:

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

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

Elianna Roach · Answer 2

The correct option is;

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

Step-by-step 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).