Question

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).

Answer 1

Interpret the functions as
f(x) = −(6/11)(11/2)^x, g(x) = (6/11)(11/2)^(−x), h(x) = −(6/11)(11/2)^(−x).

For any real x the exponential (11/2)^x is positive, so g(x) > 0 for all x (range y > 0) while f(x) and h(x) are always negative (range y < 0). All three have domain (−∞, ∞).

Thus: "The ranges of f(x) and h(x) are different from the range of g(x)."