Answer all the questions. (f) Consider f: {1,2,3} to {a,b,c} given by f(1) = a, f(2) = b, f(3) =c . Find f^(-1) . Show that (f^(-1) )^(-1) = f .

Let f be an invertible function . Then prove that (f^(-1))^(-1) = f.

If (fog) (1)=3, g(1) = 2, g(1) = 1,then show that f(2)=3.

If F : R rarr R is given by f(x) = (3-x^(3))^(1//3) then find ( fof ) x .

Consider f:R_(+) to [-5, oo) given by f(x)=9x^(2)+6x-5 . Show that f is invertible with f^(-1)(y)= ((sqrt(y+6)-1)/(3)) . Hence. Find (i) f^(-1)(10)" " (ii) y" if "f^(-1)(y)=(4)/(3) where R_(+) is the set of all non-negative real numbers.

Consider f:R_(+)to[-5,oo) given by f(x)=9x^(2)+6x-5 . Show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/(3)) . Hence , find f^(-1)(10)

Answer any three questions Let f: R to R be defined by f(x) = 3x + 5 Show that f is bijective. Find f^(-1) (1) and f^(-1) (0) .

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

If f: R to R is given by f(x) = (3 - x^(3))^(1//3) , then find (fof)x .

If f: R to R is given by f(x) = (3 - x^(3))^(1//3) , then find (fof)x .