Saved Bookmarks
| 1. |
Write the set of values of ‘a’ for which f(x) = loga x is increasing in its domain. |
|
Answer» f(x) = loga x Let x1, x2∈ (0, ∞) such that x1 < x2. \(\because\) the function here is a logarithmic function, so either a > 1 or 1 > a > 0. Case – 1 Let a > 1 x1 < x2 \(\therefore\) logax1 < logax2 \(\therefore\) f(x1) < f(x2) \(\therefore\) x1 < x2 & f(x1) < f(x2), ∀ x1, x2∈ (0, ∞) Hence, f(x) is increasing on (0, ∞). Case – 2 Let, 1 > a > 0 x1 < x2 \(\therefore\) logax1 > logax2 \(\therefore\) f(x1) > f(x2) \(\therefore\) x1 < x2 & f(x1) > f(x2), ∀ x1, x2∈ (0, ∞) Thus, for a > 1, f(x) is increasing in its domain. |
|