If f : R R such that f(x) = 5x - 3cosx - 4sinx,then function f(x)… - Vidyadip

MCQ

If f : $R$ $\rightarrow$ $R$ such that $f(x)$ = $5x - 3cosx - 4sinx$,then function $f(x)$ is

A
one-one but not onto
B
onto but not one-one
✓
one-one and onto
D
many one into

✓

Answer

Correct option: C.

one-one and onto

c
$f(x)=5 x-3 \cos x-4 \sin x$

$f^{\prime}(x)=5+3 \sin x-4 \cos x$

$-5 \leq 3 \sin x-4 \cos x \leq 5$

$0 \leq 5+3 \sin x-4 \cos x \leq 10$

function is stricitly increasing $\Rightarrow$ Range $=(-\infty, \infty)$

$\Rightarrow$ function is one-one onto.

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