The distinct linear functions that map [-1, 1] onto [0, 2] are: - Vidyadip

MCQ

The distinct linear functions that map $[-1, 1]$ onto $[0, 2]$ are:

✓
$f(x) = x + 1, g(x) = -x + 1$
B
$f(x) = x - 1, g(x) = x + 1$
C
$f(x) = -x - 1, g(x) = x - 1$
D
None of these.

✓

Answer

Correct option: A.

$f(x) = x + 1, g(x) = -x + 1$

$f(x) = -x - 1, g(x) = x - 1$
Since $f$ is invertible, range of $f =$ co $-$ domain of $f = x$
So, we need to find the range of $f$ to find $X$.
For finding the range, let $f(x) = y$
$\Rightarrow 4x - x^2 = y$
$\Rightarrow x^2 - 4x = -y$
$\Rightarrow x^2 - 4x + 4 = 4 - y$
$\Rightarrow (x - 2)^2 = 4 - y$
$\Rightarrow {x}-2=\pm4-{y}$
$\Rightarrow {x}=2\pm4-{y}$
This is defined only when $4-{y}\geq0$
$\Rightarrow {y}\leq4,$
$X =$ Range of $f =(-\infty,4]$

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

More "M.C.Q (1 Marks)" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The number of solutions of the differential equation $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$, is

The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=1+\text{x}+\text{y}^{2}+\text{xy}^{2}, \text{y}=(0)$ is:

$\text{y}^{2}=\text{exp}\big(\text{x}+\frac{\text{x}^{2}}{2}-1\big)$
$\text{y}^{2}=1+\text{C}\ \text{exp}\Big(\text{x}+\frac{\text{x}^{2}}{2}\Big)$
$\text{y}=\tan (\text{C}+\text{x}+\text{x}^{2})$
$\text{y}=\tan\Big(\text{x}+\frac{\text{x}^{2}}{2}\Big)$

For a binomial variate X, if $\text{n}=3$ and $\text{P(X}=1)=8\text{ P(X = 3}),$ then p =

The value of (adj A) is equal to

2A
4A
8A
16A

Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is

Choose the correct option from given four options:
$\int\frac{\text{x}+\sin\text{x}}{1+\cos\text{x}}\text{dx}$ is equal to:

$\log|1+\cos\text{x}|+\text{C}$
$\log|\text{x}+\sin\text{x}|+\text{C}$
$\text{x}-\tan\frac{\text{x}}{2}+\text{C}$
$\text{x}\cdot\tan\frac{\text{x}}{2}+\text{C}$

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta, \alpha, \beta \in L$. Then, $R$ is

The maximum value of Z = 3x + 4y subjected to contraints $\text{x}+\text{y}\leq40,\text{x}+2\text{y}\leq60,\text{x}\geq0$ and $\text{y}\geq0$ is:

The degree and the order of the differential equation:
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\sqrt{1}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^3\text{ are:}$

2 and 3.
3 and 2.
2 and 2.
3 and 3.

If $\text{f(x)}=\frac{1-\sin\text{x}}{(\pi-2\text{x})^2},$ when $\text{x}\neq\frac{\pi}{2}=\lambda$ then f(x) will be continuous function at $\text{x}=\frac{\pi}{2},$ where $\lambda=$

$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{2}$
none of these