Functions

1 Mark and 2 Mark questions :

Please note that  / stands for divison

1) If Function f: R-{2} -> R is defined as f(x)=(2x+1/x-2 )then prove that f(2x+1/x-2)= x

2) f: A->B and f have inverae function f^-1: B->A. then state the properties of f for which its inverse exist?

3) Let f:R->R; g: R->R defined f(x)=1+2x ; g(x)=3-2x find fog(3)?

4) If f(x)=2x+3 , then find the value of f(x+h)-f(x) / f(x)  (h ≠ 0)

5)  If function f;R-{1} -> R is defined as f(x)=(x+1/x-1) ; then prove that f(x) + f(1/x) =0 (x ≠ 0)

6)  If f(x)=(1-x/1+x) find f(0),f(1),f(2) and f(3)

7)  If f(x) = x+2 ; g(x)= x²-x-2 then find g(1)+g(2)+g(3)

                                                             f(-4)+f(-2)+f(2)

8) If f={(1,3)(2,5)(3,7)} ; g={(3,7)(5,9)(7,10)} find gof

9) Define one-one function show that f(x)=3x-2 x ∈N is one to one

10) If f: R-{3} -> R is defined by f(x)=(x+3/x-3) show that f(3x+3/x-1) =x for x ≠ 1

11) Define the following 1) one to one function 2) Onto function 3) constant function 4) Bijection function

4 Mark Questions :

12 ) Let f,g,h be the functions defined as following f(x)=x+2;g(x)=3x-1; h(x)=2x then show that h0(g0f)=(h0g)0f
13)  If f:R->R define as f(x)=2x+3 ,show that f^-1 is a function and find f^-1(4)
14) let f be given by f(x) =x+2 and  f has the domain { x: 2 ≤ x ≤ 5} find f^-1 and its domain and range
15) Given f(x)=1+2x ; g(x)=3-2x ∀x ∈R find f0g(x),gof(x) ; gof(3);fog(3)
16) Let f,g,h are the functions defined by f(x)=x ;g(x)=1-x and h(x)=x+1 find 1) (h0g) 0f 2) h0(gof) then waht you observe from 1 and 2
17) let f(x)=x-1;g(x)=x²-2 ; h(x) =x³-3 then prove that f0(g0h) = (f0g)0h
18) if f(x)=x+2 ; g(x)=x ;h(x)=x² then shoe that (h0g)0f=h0(g0f)