Show that the logarithmic function f:R0^+ R given by f(x) = loga … - Vidyadip

Question

Show that the logarithmic function $\text{f}:\text{R}0^+\rightarrow \text{R}$ given by f(x) = log_a x, a > 0 is a bijection.

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Answer

We have, f : A → B and g : B → C are one-one functions.
Now we have to prove: gof : A → C in one-one.
Let $\text{x, y}\in\text{A}$ such that
gof(x) = gof(y)
⇒ g(f(x)) = g(f(y))
⇒ f(x) = f(y) [$\because$ g in one-one]
⇒ x = y [$\because$ f in one-one]
$\therefore$ gof is one-one function.

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