Consider `f : {1, 2, 3} rarr {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`

Let f : { 1, 2, 3} rarr {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} rarr { 1, 2, 3} such that gof = I_x and fog = l_y . where X = {1, 2, 3} and Y = {a, b, c} .

Consider f:(1,2,3) rarr (a,b,c) and g:(a,,c) rarr (apple, ball, cat) defined as f(1) = a,f(2) = b, f(3) = c, g (a) = apple, g (b) = ball, g(c ) = cat. Find (gof)

If f : R rarr R be given by: f(x) = (3-x^3)^1//3 , then f(f(x)) is:

If f : R rarr R given by f(x) = x^3 + 2 , then f^-1(x) equals :

If f(x) = log (2x-1), find f'( c ) .

Consider f : R_+rarr [4, oo) given by f (x) = x^2 + 4 Show that f is invertible with the inverse f ^–1,of f given by f ^–1(y) = sqrt(y - 4) , where R_+ is the set of all non-negative real numbers.

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).

Show that the function f: N rarrN given by f(1) = f(2) = 1 and f(x) = x-1 AAxgt2 is onto but not one-one.

Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x) =x-1 , for every x > 2 is onto but not one-one.

Consider f : R → R given by f(x) = 4x + 3 . Show that f is invertible. Find the inverse of f.