Let f: R`rarr` R be defined by f(x) = 2x - 3 and g: R `rarr` R be defined by g(x) =`(x+3)/(2)` , show that fogʻ= `I_(R)`

Let f: RrarrR defined by f(x)=x+1 and g:R rarr R defined as g(x)= sqrtx find fog and gof if defined.

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

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

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 : R rarr R is given by f(x) = x^(2) +2 and g:R rarr R is given by g(x) = (x)/(x-1), x ne 1 then find fog and gof and hence find fog (2) and gof (-3) .

Show that if f : R - {(7)/(5)} rarr R- {(3)/(5)} is defined by f (x) = (3x+4)/(5x-7) andc g:R - {(3)/(5)} rarr R - {(7)/(5)} is defined by g(x) = (7x+4)/(5x-3) then fog = I_(A) and gof = I_(B) where A = R - {(3)/(5)} B=R - {(7)/(5)} , I_(A) (x) = x AA x in A and I_(B) (x) =x AA x in B are called identity functions on sets A and B respectively.

Consider a function f : [ 0, (pi)/(2)] rarr R given by f(x) = sinx and g : [0,(pi)/(2)] rarr R given by g(x) = cos x . Show that f and g are one -one but f+g is not one - one .

If f:RrarrR and g:RrarrR is defined by f(x)=sinx and g(x)=5x^2 , then (gof)(x).