Let f: [0,1) `rarr` [ 0,1] be defined by
f(x) = `{{:(x, "if x is if x is rational "),(1-x, "if x is irrational "):}`
Then find fof (x) .

Show that the function f defined by f(x)={(x if "x is rational"),(-x if "x is irrational"):} is continuous at x=0 AAxne0inR

Show that the function f defined by f(x)={(1 if "x is rational"),(0if "x is irrational"):} is discontinuous AAne0inalpha

Show that the function f defined by f(x)={(x if "x is rational"),(0 if "x is irrational"):} is discontinuous everywhere except at x=0.

If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

Let f:Rto(-1,1) be defined by f(x)=x/(1+x^2),x in R . Find f^(-1) if exists.

Let f:R rarr R be defined by f(x) = x^(2) +1 Then, find pre-images of 17 and - 3.

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.

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

Let f : R rarr R be defined by f (x) = (x)/(sqrt(1+x^(2))) AA x in R . Then find ( fofof ) (x) . Also show that fof ne f^(2) .

If the function f:[1, oo) rarr [ 1,oo) defined by f(x) = 2^(x(x -1)) is invertible, then find f^(-1) (x).