Let `f: X rarr Y` be a function defined by f(x) = a sin ( x +`pi/4`) + c. If f is both one-one and onto, then find the set X and Y

Let f: XtoY be a function defined by f(x) =asin(x+(pi)/4) + bcosx + c. If f is both one-one and onto, find set X and Y.

Let f:R rarr B be a functio defined by f(x)=tan^(-1).(2x)/(1+x^(2)) , then f is both one - one and onto when B is in the interval

Let f:(-1,1)rarr B be a function defined by f(x)=tan^(-1)((2x)/(1-x^(2))). Then f is both one- one and onto when B is the interval

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval

Let f:[-1,1] rArr B be a function defined as f(x)=cot^(-1)(cot((2x)/(sqrt3(1+x^(2))))) . If f is both one - one and onto, then B is the interval

A function f:RrarrR is defined by f(x)=4x^(3)+5,x inR . Examine if f is one-one and onto.

A function f:RrarrR be defined by f(x) = 5x + 6, prove that f is one-one and onto.

The function f:[2,oo)rarr Y defined by f(x)=x^(2)-4x+5 is both one-one and onto if

Let f:R rarr [0, (pi)/(2)) be a function defined by f(x)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

Show that the function f : R rarr R defined by f(x) = cos (5x+3) is neither one-one not onto.