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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The function ${x^5} - 5{x^4} + 5{x^3} - 1$ is

A circle has the same centre as an ellipse and passes through the foci $F_1 \& F_2$ of the ellipse, such that the two curves intersect in $4$ points. Let $'P'$ be any one of their point of intersection. If the major axis of the ellipse is $17 $ and the area of the triangle $PF_1F_2$ is $30$, then the distance between the foci is :

The vertex of the parabola ${x^2} + 8x + 12y + 4 = 0$ is

On each face of a cuboid, the sum of its perimeter and its area is written. Among the six numbers so written, there are three distinct numbers and they are $16,24$ and $31$.The volume of the cuboid lies between

The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$

Let $f(x)$ be continuous and differentiable function for all reals.$f\left( {x + y} \right) = f\left( x \right) - 3xy + f\left( y \right)$. If $\mathop {\lim }\limits_{h \to 0} \frac{{f\left( h \right)}}{h} = 7$ then the value of $f'\left( x \right)$ is

$\int_{\, - \,2}^{\,2} {\,\left| {\,[x]\,} \right|\,dx = } $

Let $\overrightarrow{\mathrm{a}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $(\vec{a}+\vec{b}) \times \vec{c}=2(\vec{a} \times \vec{b})+24 \hat{j}-6 \hat{k}$ and $(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}+\hat{\mathrm{i}}) \cdot \overrightarrow{\mathrm{c}}=-3$. Then $|\overrightarrow{\mathrm{c}}|^2$ is equal to_______.

If focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$ , such that $a$ , $b$ , $c$ are in $H.P.$ , then value of $b$ is equal to

If the arithmetic mean and geometric mean of the $p ^{\text {th }}$ and $q ^{\text {th }}$ terms of the sequence $-16,8,-4,2, \ldots$ satisfy the equation $4 x^{2}-9 x+5=0,$ then $p+q$ is equal to ..... .