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Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsFunctions3 Marks
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.
✓

Answer

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

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