What are the values of ‘a’ for which f(x) = a^x is decreasing on R?

f(x) = a^x

f’(x) = a^x log a

f(x) is decreasing on R.

f’(x) < 0, ∀x ϵ R

a^x log a < 0, ∀x ϵ R

Logarithmic function is not defined for negative values of a.

a^x > 0

a^x log a < 0 can be possible when log a < 0, ∀x ϵ R.

1 > a > 0

Hence the function f(x), whose values are 1 > a > 0.