Question

③ Find the range of the following function.
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Answer 1

Answer:

Step-by-step explanation:

Given function,

$f(x) = log_{4} (x + \frac{1}{x})$

We know that $x + \frac{1}{x} \geqslant 2$

Taking log both sides with base 4,

$\implies log_{4} (x + \frac{1}{x}) \geqslant log_{4}(2)$

$\implies log_{4} (x + \frac{1}{x}) \geqslant \frac{1}{2}$

Hence, $Range(f) \in [\frac{1}{2} , \infty)$