Sample QuestionsRelations and Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $f: R \rightarrow R , f(x)=\sin x$ and $g: R \rightarrow R , g(x)=x^2$ then $(f o g)(x)$ is equal to :
View full solution →A function $f: R \rightarrow R$ is defined such that $f(x)=2+$ $x^2$ then $f$ is :
View full solution →Suppose $X =\left\{x^2, x \in N\right\}$ and $f: N \rightarrow X$ defined such that $f(x)=x^2, x \in N$ then function is:
View full solution →If $A=\{1,2,3\}$ and a relation $R$ is such that$R =\{(1,3),(2,2),(3,2)\}$ then for making R reflexive and symmetric set of minimum ordered pair is :
View full solution →If $R =\left\{(x, y): x, y \in Z , x^2+y^2 \leq 4\right\}$ is a relation in Z then domain of R is :
View full solution →$f(x)=2 x, f: N \rightarrow N$, show that $f(x)$ is not onto.
View full solution →By $f(x)=2 x,$ defined a function $f : A \rightarrow B$ is one $-$ one and onto both. If $A =\{1,2,3,4\}$ then find set $B$.
View full solution →If $A=\{1,2\}$ and $B=\{3,4\}$, Find the number of relations in A and B ?
View full solution →Is $f: Z \rightarrow Z, f(x)=x^2$ is one-one function?
View full solution →In set $A=\{0,1,2,3,4,5\} R$ is equivalence relation where $R =\{(a, b):(a-b)$ is divisible by 2$\}$. Write equivalence class [0].
View full solution →A function $f: R \rightarrow R$ given by $f(x)=2 x+3$. Prove that $f$ is invertible.
View full solution →Prove that in set $Z$ relation $R$ defined as $a R b$ $\Leftrightarrow a-b$ is divisible by 3 , is equivalence relation.
View full solution →Prove that $f: R \rightarrow R , f(x)=x^3+x$ is one-one onto function.
View full solution →Suppose $A=R-\{2\}$ and $B=R-\{1\}$, if a function $f: A \rightarrow B$ is defined such that $f(x)=\frac{x-1}{x-2}$, then prove that $f$ is one-one onto.
View full solution →If $f, g: R \rightarrow R$ function is defined such that $f(x)=x^2+1, g(x)=2 x-3$ then find $f o g(x)$, gof $(x)$ and $\operatorname{gog}(3)$.
View full solution →To confirm that, Is every real number in $R$. $R =\{(a, b): a, b \in R$ and $a-b+\sqrt{3} \in S \}$ where $S$ is set of all irrational numbers, defined, $R$ is reflexive, symmetric and transitive.
View full solution →In set $I \times I _0$, relation $R$ is defined such that $(a, b)$ $R (c, d) \Leftrightarrow a d=b c$ if $I _{ 0 }$ is set of non-zero integers. Then prove that $R$ is equivalence relation.
View full solution →In set of real numbers, a relation $R_1$ is defined such that $(a, b) \in R _1 \Leftrightarrow 1+a \cdot b>0 \forall a, b \in R$ prove that $R_1$ is reflexive and symmetric but not transitive.
View full solution →Suppose $N$ is set of natural numbers and $R$, is defined in $N \times N$ such that :
$(a, b) R (c, d) \Leftrightarrow a d(b+c)=b c(a+d)$. Prove that $R$ in equivalence in $N \times N$.
View full solution →If function $f: R \rightarrow R , f(x)=x^2+2$ and $g: R \rightarrow R$ $g(x)=\frac{x}{x-1}, x \neq 1$ then find $f o g$ and $g o f$ and also find $( fog )(2)$ and $( gof )(-3)$ ?
View full solution →$f(x)=2 x$, for $f: N \rightarrow N$, is. ________ but not onto.
View full solution →Total number of one-one functions defined from set $A =\{a, b, c\}$ to set $B =\{x, y, z, t\}$ is. ________
View full solution →From set $A =\{1,2,3,4\}$ to set $B =\{a, b, c\}$ defined total number of functions are. ________
View full solution →$f: X \rightarrow Y$ is onto function, if and only if. _________ of $f$ $= Y$.
View full solution →Function $f: X \rightarrow Y$ is known as _________, if for every $y \in Y$ a element $x$ has in existence is X such that $f(x)$ $=y$.
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