Into Function

Q. A function f(x) is an into function if and only if the range of f is a of its co-domain.

1. superset
2. proper subset
3. subest

Q.

What should be the relation between range and codomain of a function, for a function to be an into function -

1. Range < Co domain

2. Range > Co domain

3. Range = Co domain

4. None of the above.

Q. Which of the following functions are into functions if they are all defined from $R$ to $R$?

1. $f\left(x\right)=\text{sin}x$
2. $f\left(x\right)=\text{cos}x$
3. $f\left(x\right)=e^x$
4. $f\left(x\right)=x^3$

Q. The largest set of real values of ${}^{\prime }{x}^{\prime }$ for which $ln(1+x)\le x$ is

1. $(-1,\infty )$
2. $(-1,0)\cup (0,\infty )$
3. $[0,\infty )$
4. $(0,\infty )$

Q.

Which of the following function is an into function if all are defined on f: R $\to$ R

1. f(x) = sin(x)

2. f(x) = cos(x)

3. f(x) = $e^x$

4. All of the above

Q. If $\overline{a}\times \overline{i}+2\overline{a}-4\overline{i}-2\overline{j}+\overline{k}=0$, then $\overline{a}=$

1. $2\overline{j}+\overline{k}$
2. $2\overline{j}-\overline{k}$
3. $2\overline{i}+\overline{j}$
4. $2\overline{i}-\overline{j}$

Q.

Function f(x) = {x} on f: R $\to$ R where {} is fractional part function, is an into function.

1. True

2. False

Q.

Which of the following function is an into function if all are defined on f: R $\to$ R

1. All of the above

2. f(x) = sin(x)

3. f(x) = cos(x)

4. f(x) = e^x

Q.

Function f(x) = {x} on f: R $\to$ R where {} is fractional part function, is an into function.

1. True

2. False

Q. If A = { a, b, c, d, e}, B = { c, d, e, f }, C = {b, d}, D = { a, e}
then the following statement is true or false?
$D\subseteq B$