f(w)={[2x,," if "x<0],[u_(x),,0<=x<=1],[x>1]

Let f:W->W , be defined as f(x)=x-1 , if x is odd and f(x)=x+1 , if x is even. Show that f is invertible. Find the inverse of f , where W is the set of all whole numbers.

Let f:W rarr W, be defined as f(x)=x-1, if x is odd and f(x)=x+1, if x is even.Show that f is invertible.Find the inverse of f, where W is the set of all whole numbers.

Evaluate: int_(-1)^1f(x)dx ,w h e r ef(x)={1-2x ,xlt=0 1+2x ,xgeq0 int_(-1)^4f(x)dx ,w h e r ef(x)={2x+8,1lt=xlt=2 6x ,2lt=xlt=4

Let W = N cup {0} . Suppose f : W to W is a function such that f(0)=0, f(1) = 1,f(2) =2 and f(x) = f(x-2) + f(x-3) for x=3,4,……….. Then f(9) =……………..

Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +1 if x is even then show that f is invertible. Find the inverse of f where W is the set of all whole numbers.

Evaluate the following w.r.t x: If f'(x)= 4 x^3 - 3 x^2 +2x +k, f(0)=1 and f(1)=4, find f(x)

Let f:W rarr W is defined as f(x)={:{ (x/2 ,x = 2n-2, n in N), (0, x=2n-1, n in N) :} .Then the number of points lying on both y=f(f(x)) and x -axis, x in[0,10] ,is