Let f: [- 2 , 2 ] A be defined by f(x)= sinx. If f is a bijection… - Vidyadip

Question

Let $\text{f}:\Big[-\frac{\pi}{2},\frac{\pi}{2}\Big]\rightarrow\ \text{A}$ be defined by f(x)= sinx. If f is a bijection, write set A.

✓

Answer

$\because$ f is a bijection,Co-domain of f = range of f
As $-1\leq\sin\text{x}\leq1,$
$-1\leq\text{y}\leq1$
Therefore, A = [-1, 1]

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 "2 Marks Questions" from Functions→Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the definite integral$\int_{0}^{\frac{\pi}{2}} \cos 2 x d x$

Find the angle between the pair of lines
$\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$
$\frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2}$

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\frac{\text{x}}{\text{x}+1}\text{ dx}$

Evalute the following integrals:
$\int\frac{1-\sin2\text{x}}{\text{x}+\cos^2\text{x}}\text{dx}$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
${3}\sqrt{\frac{\text{d}^2\text{y}}{\text{dx}^2}}=\sqrt{\frac{\text{dy}}{\text{dx}}}$

Define vector product of two vectors.

If $\vec{\text{a}},\vec{\text{b}}$ are two vectors, then write the truth value of the following statement:$\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|\Rightarrow\vec{\text{a}}=\vec{\text{b}}$

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that,

The youngest is a girl.
At least one is a girl?

Find x, y, z and t, if.
$2\begin{bmatrix}\text{x}&5\\7&\text{y}-3\end{bmatrix}+\begin{bmatrix}3&4\\1&2\end{bmatrix}=\begin{bmatrix}7&14\\15&14\end{bmatrix}$

Define a transitive relation.