Short Question for XII

FUNCTION

EXERCISE -1

1) If A{1,2,3} and B ={a,b}, Write total number of functions from A to B. 8

2) If A{a,b,c} and B ={-2,-1,0,1,2}, Write total number of one-one functions from A to B. 60

3) Write total number of one-one functions from set A I={1,2,3,4} to set B ={a,b,c}. 0

4) If f: R--> R is defined by f(x)= x², Write f⁻¹(25). {-5,5}

5) If f: C--> C is defined by f(x)= x², Write f⁻¹(-4). Here C denotes the set of all complex numbers. {2i, -2i}

6) If f: R--> R is defined by f(x)= x³, Write f⁻¹(1). {1}

7) Let C denote the set of all complex numbers. A function f: C--> C is defined by f(x)= x³, Write f⁻¹(-1). {1, w,w²}

8) Let f be a function from C(set of all complex numbers) to itself defined by f(x)= x³, Write f⁻¹(-1). {-1,- w,-w²}

9) Let f: R--> R is defined by f(x)= x⁴, Write f⁻¹(1). {-1,1}

10) Let f: C--> C is defined by f(x)= x⁴, Write f⁻¹(1). {-1,-i, 1,i}

11) If f: R--> R is defined by f(x)= x², Write f⁻¹(-25). ¢

12) If f: C--> C is defined by f(x)= (x-2)³, Write f⁻¹(-1). {1,2,-w,2-w²}

13) If f: R--> R is defined by f(x)= 10x -7,, Write f⁻¹(x). (x+7)/10

14) Let f: (- π/2, π/2) --> R be a function is defined by f(x)= [cos x], Write range of (f) . {1, cos 1, cos 2}

15) If f: R--> R is defined by f(x)= 3x -4 Write f⁻¹(x). (x+4)/3

16) If f: R--> R g: R--> R are given by f(x)= (x +1)² and g(x)= x²+1, then write the value of gog(-3). 121

17) Let A= {x belongs to R: -4≤x ≤ 4 and x ≠ 0} and f: A--> R be defined by f (x)= |x|/x. Write the range of f. {-1,1}

18) Let f: (- π/2, π/2) --> A be defined by f(x)= sin x. If f is a bijection, write set A. A[-1,1]

19) If f: R--> R⁺ is defined by f(x)=a ˣ, a> 0 and a≠ 1. Write f⁻¹(x). Logₐ x

20) Let f: R--{-1}--> R--{1} is defined by f(x)= x/(x+1). Write f⁻¹(x). x/(1-x)

21) Let f: R--{-3/5}--> R--{1} be a function defined by f(x)= 2x/(5x+3). Write f⁻¹: Range of f --> R --{-3/5}. 3x/(2 - 5x)

22) Let f: R--> R, g: R--> R be two functions defined by f(x)= x²+x+1 and g(x)= 1 - x². Write fog(-2). 7

23) Let f: R---> R be defined by f(x)= (2x- 3)/4. Write fof⁻¹(1). 1

24) Let f be an invertible real function. Write (f⁻¹of)(1)+ (f⁻¹of)(2)+....(f⁻¹of)(100). 5050

25) Let A={1,2,3,4} and B={a,b} be two sets. Write total number of onto functions from A to B. 14

26) Write the domain of the real function f(x)= √{x - [x]}. R

27) Write the domain of the real function f(x)= √{[x] - x}. ¢

28) Write the domain of the real function f(x)= 1/√{|x| - x}. (- ∞ ,0)

29) Write whether f: R---> R given by f(x)= x + √(x²) is one-one, many-one, onto or into. Many one into 

30) If f(x)= x+7 and g(x) =x-7, x belongs to R, write fog(7). 7

EXERCISE -2