Q2 of 96 Page 17

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

f(x) = ax


f’(x) = ax log a


f(x) is decreasing on R.


f’(x) < 0, ∀x ϵ R


ax log a < 0, ∀x ϵ R


Logarithmic function is not defined for negative values of a.


ax > 0


ax 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.


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