Consider the three functions below.
f(x) = negative startfraction 6 over 11 endfraction (eleven-halves) superscript x g(x) = startfraction 6 over 11 endfraction (eleven-halves) superscript negative x h(x) = negative startfraction 6 over 11 endfraction (eleven-halves) superscript negative x
which statement is true?
the range of h(x) is y > 0.
the domain of g(x) is y > 0.
the ranges of f(x) and h(x) are different from the range of g(x).
the domains of f(x) and g(x) are different from the domain of h(x).

OPTION C.The ranges of f(x) and h(x) are different from the range of g(x).

Step-by-step explanation:

The range of g(x) is y > 0

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

Step-by-step explanation:

we have

Using a graphing tool

see the attached figure

Verify each statement

case A) The range of h(x) is y > 0.

The statement is false

The range  of h(x) < 0

case B) The range of g(x) is y > 0.  (Note the statement is The range of g(x) is y > 0 instead of  The domain of g(x) is y > 0)

The statement is true (see the attached figure)

case C) The ranges of f(x) and h(x) are different from the range of g(x)

The statement is true (see the attached figure)

Because

The ranges of f(x) and h(x) are y < 0

and

The range of g(x) is y > 0

case D) The domains of f(x) and g(x) are different from the domain of h(x)

The statement is false

The domain of the three functions is the same