Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsDomain-RangeMedium2 minQB

MathematicsMediumsingle choice

Range of $f (x) = lo g_{310} (5 (2 sin x + cos x) + 5)$ is

Answer:

Solution:

We know that:

$- 5 \leq 2 sin x + cos x \leq 5, \forall x \in R$

$\Rightarrow - 5 \leq 5 (2 sin x + cos x) \leq 5$

$\Rightarrow 0 \leq 5 (2 sin x + cos x) + 5 \leq 10$

$\Rightarrow - \infty < lo g_{310} (5 (2 sin x + cos x) + 5) \leq 3$

Hence, the range is $(- \infty, 3]$ .

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: QB

Loading discussions...