Short Quiz

Question 1 of 5

NCERT Exemplar

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined by $f(x)=3 x-4$. Then $f^{-1}(x)$ is given by

A $\frac{x+4}{3}$ B $\frac{x}{3}-4$ C $3 x+4$ D None of these

Select one option. Answers are shown after the test.

Question 2 of 5

NCERT Exemplar

Let $f:[2, \infty) \rightarrow \mathbf{R}$ be the function defined by $f(x)=x^2-4 x+5$, then the range of $f$ is

A R B $[1, \infty)$ C $[4, \infty)$ D $[5, \infty)$

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Question 3 of 5

NCERT Exemplar

Let $\mathrm{A}=\{1,2,3\}$ and consider the relation
$$ R=\{1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\} . $$
Then $R$ is

A reflexive but not symmetric B reflexive but not transitive C symmetric and transitive D neither symmetric, nor transitive

Select one option. Answers are shown after the test.

Question 4 of 5

NCERT Exemplar

Let us define a relation R in $\mathbf{R}$ as $a \mathrm{R} b$ if $a \geq b$. Then R is

A an equivalence relation B reflexive, transitive but not symmetric C symmetric, transitive but D neither transitive nor reflexive not reflexive but symmetric.

Select one option. Answers are shown after the test.

Question 5 of 5

NCERT Exemplar

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be given by $f(x)=\tan x$. Then $f^{-1}(1)$ is

A $\frac{\pi}{4}$ B $\left\{n \pi+\frac{\pi}{4}: n \in Z\right\}$ C does not exist D none of these

Select one option. Answers are shown after the test.

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