Q. 35.0( 1 Vote )

Write the set of values of ‘a’ for which f(x) = loga x is increasing in its domain.

Answer :

f(x) = logax


Let x1, x2ϵ (0, ∞) such that x1 < x2.


the function here is a logarithmic function, so either a > 1 or 1 > a > 0.


Case – 1


Let a > 1


x1 < x2


logax1 < logax2


f(x1) < f(x2)


x1 < x2 & f(x1) < f(x2), x1, x2ϵ (0, ∞)


Hence, f(x)is increasing on (0, ∞).


Case – 2


Let, 1 > a > 0


x1 < x2


logax1 > logax2


f(x1) > f(x2)


x1 < x2 & f(x1) > f(x2), x1, x2ϵ (0, ∞)


Thus, for a > 1, f(x) is increasing in its domain.


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