If `A={1,2,3,4}`. Prove that `f` defined by `f={(x,y) , x+y=5}` is function from `A` to `A`

Prove that f(x) given by f(x+y)=f(x)+f(y)AA x in R is an odd function.

Consider set A = {x_(1), x_(2), x_(3), x_(4), x_(5)} and set B = {y_(1), y_(2), y_(3)} . Function f is defined from A to B. Number of function from A to B such that f(x_(1)) = y_(1) and f(x_(2)) != y_(2) is

Consider set A={x_(1),x_(2),x_(3),x_(4)} and set B={y_(1),y_(2),y_(3)} Function f is defined from A to B

If A={1,2,3,4}" and "B={1,2,3,4,5,6} are two sets and function f: A to B is defined by f(x)=x+2,AA x in A , then the function f is

(a) If f:RrarrR defined by f(x)=(3x+5)/(2) is an invertible function, find f^(-1) . Show that f:RrarrR defined by f(x)=(4x-3)/(5),x inR is invertible function and find f^(-1) .

Let A={x_1,x_2,x_3,x_4,x_5},B={y_1,y_2,y_3,y_4}, Function f is defined from A to B. Such that f(x_1)=y_1, and f(x_2)=y_2 then, number of onto functions from A to B is (A) 12 (B) 6 (C) 18 (D) 27

If y=f(x)=(3x+1)/(5x-3) , prove that x=f(y).

Prove that the function f: R->R defined as f(x)=2x-3 is invertible. Also, find f^(-1) .