A bijective function is both one-one and onto. (True/False)

Show that f : N rarr N given by : f(x) = {x+ 1, if x is odd x - 1 , if x is even is both one-one and onto.

Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,if x is even,,):} is both one-one and onto.

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these

Let f: A -> B and g : B -> C be two functions and gof: A -> C is define statement(s) is true? a. If gof is one-one, then f anf g both are one-one b. if gof is one-one, then f is one-one c. If gof is a bijection, then f is one-one and g is onto d. If f and g are both one-one, then gof is one-one.

If f:R to R be defined by f(x) =2x+sinx for x in R , then check the nature of the function. a. one-to-one and onto b. one-to-one but not onto c. onto but not one-to-one d. neither one-to-one nor onto

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

True or false In an LPP, the objective function is always a linear function.

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

In the following case, state whether the function is one-one, onto or bijective. Justify your answer: f:RrarrR defined by f(x) = 3-4x