Consider `f" ":" "{1," "2," "3}->{a ," "b ," "c}` given by `f(1)" "=" "a` , `f(2)" "=" "b` and `f(3)" "=" "c` . Find `f^(-1)` and show that `(f^(-1))^(-1)=" "f` .

Given f(x)=3x+2 . Find f^(-1)(x)

Let f : {1, 2, 3}->{a , b , c} be one-one and onto function given by f (1) = a , f (2) = b and f (3) = c . Show that there exists a function g : {a , b , c}->{1, 2, 3} such that gof=I_x and fog=I_y

If f(x) = ax^2+bx+c and f(1)=3 and f(-1)=3, then a+c equals

Consider f : R->{-4/3}->R-{4/3} given by f(x) = (4x+3)/(3x+4) . Show that f is bijective. Find the inverse of f and hence find f^(-1)(0) and x such that f^-1(x) = 2 .

If f(x)=1-4x , and f^(-1)(x) is the inverse of f(x), then f(-3)f^(-1)(-3)=

If f:R->R be defined by f(x)=x^2+1 , then find f^(-1)(17) and f^(-1)(-3) .

Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} and g:{a ,\ b ,\ c}-> {apple, ball, cat} defined as f(1)=a ,\ \ f(2)=b ,\ \ f(3)=c ,\ \ g(a)= apple, g(b)= ball and g(c)= cat. Show that f,\ g\ a n d\ gof are invertible. Find f^(-1),\ g^(-1) and (gof)^(-1) and show that (gof)^(-1)=f^(-1)o\ g^(-1) .

Let f : R rarr given by f(x) = 3x^(2) + 5x + 1 . Find f(0), f(1), f(2).

If f: C->C is defined by f(x)=(x-2)^3 , write f^(-1)(-1) .

If f(x)=log((1-x)/(1+x)) , show that f(a)+f(b)=f((a+b)/(1+ab))