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KC Sinha Solution Class 12 Chapter 2 Functions ( फलन ) Exercise 2.2 (Q1-Q15)

 Exercise 2.2

Question 1

If the functions f and g are given by

\begin{aligned}&f=\{(1,2),(3,5),(4,1)\} \\&g=\{(2,3),(5,1),(1,3)\}\end{aligned}

then define fog and gof

Sol :



Question 2

Let A=\{1,2,3\}, B=\{4,5\}, C=\{5,6\}.

Let f: A \rightarrow B, g: B \rightarrow C be defined by f(1)=4, f(2)=5, f(3)=4, g(4)=5, g(5)=6 Find gof : A \rightarrow C.

Sol :


Question 3

Let the functions f and g be given by f=\{(1,-1),(2,-4),(3,-9)\} and g=\{(-1,3),(-4,7),(-9,11)\}. Show that gof is defined while fog is not defined, Also find gof

Sol :



Question 4

Let f: \mid a, c, d\} \rightarrow\{a, b, e\} and g:\{a, b, e\} \rightarrow\{a, c\} be given by f=\{(a, b),(c, e),(d, a)\} and g=\{(a, c),(b, c),(e, a)\} write down

(i) gof

(ii) fog

Sol :



Question 5

Let A=\{a, b, c, d\}, B=\{p, q, r, s\}, C=\{x, y, z\}

Let f: A \rightarrow B and g: B \rightarrow C be defined as

f(a)=p, f(b)=q, f(c)=r, f(d)=s

and g(p)=x, g(q)=x, g(r)=y, g(s)=z

Find gof : A \rightarrow C

Sol :


Question 6

Let f:\{2,3,4,5\} \rightarrow\{3,4,5,9\} and

g:\{3,4,5,9\} \rightarrow\{7,11,15\} be functions defined as

f(2)=3, f(3)=4, f(4)=f(5)=5

and g(3)=g(4)=7 and g(5)=g(9)=11.

Find gof.

Sol :



Question 7

If f: R \rightarrow R and g: R \rightarrow R are given by f(x)=\cos x and g(x)=3 x^{2}, find gof and fog and show that gof ≠ fog

Sol :


Question 8

If f(x)=8 x^{3} and g(x)=x^{1 / 3}, find g o f and f o g.



Question 9

Let f: R \rightarrow R and g: R \rightarrow R be defined by f(x)=x^{2}+2 x-3, g(x)=3 x-4, find (g o f)(x) and (f o g)(x).


Question 10

Let R be the set of all real numbers. If the functions f: R \rightarrow R and g: R \rightarrow R are given by f(x)=x^{2}+x+1 and g(x)=2 x for all x \in R, find

(i) fog

(ii) gof

(iii) fof

(iv) gog.




Question 11

Consider f: N \rightarrow N, g: N \rightarrow N and h: N \rightarrow R defined as f(x)=2 x, g(y)=3 y+4 and h(z)=\sin z, \forall x, y, z \in N. Show that ho (g o f)=(h o g) of. 


Question 12

Let f: R \rightarrow R be defined by f(x)=2 x-3 and g: R \rightarrow R be defined by g(x)=\frac{x+3}{2}

Show that f o g=I_{R}=g o f.



Question 13

Let f: A \rightarrow B and g: B \rightarrow C be two one-one functions. Show that g o f is also a one-one function.



Question 14

If f(x)=x+7 and g(x)=x-7, x \in R, find (f o g)(7).



Question 15

If the function f: R \rightarrow R be given by f(x)=x^{2}+2 and g: R \rightarrow R be given by g(x)=\frac{x}{x-1}, x \neq 1, find fog and gof and hence find f o g(2) and g o f(-3).








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