If and are two positive increasing functions

MATHEMATICS · Multi correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

f(x)

and

g(x)

are two positive increasing functions, then (1)

(f(x))^{g(x)}

is always increasing. (2) If

(f(x))^{g(x)}

is decreasing, then

f(x)<1

. (3) If

(f(x))^{g(x)}

is increasing, then

f(x)>1

. (4) If

f(x)>1

, then

(f(x))^{g(x)}

is increasing.