Answer to Question #234555 in Discrete Mathematics for Reddy mounika

Question

Define a bijective function. Explain with reasons whether the following functions are bijective or not. Find also the inverse of each of the functions.
i. f(x) = 4x+2, A=set of real numbers
ii. f(x) = 3+ 1/x, A=set of non zero real numbers
iii. f(x) = (2x+3) mod7, A=N7

Answer 1

$A function f: A→B \space is \space bijective (or \space f \space is \space a \space bijection) \space if each \space b∈B \space has \space exactly \space one \space preimage.$

i)

$f(x) = 4x+2\\ For \space any \space set \space A, the \space identity \space function \space A \space is \space a \space bijection$

ii)

$f(x) = \frac{3+ 1}{x}\\ For \space any \space set \space A, the \space identity \space function \space A \space is \space a \space bijection$

iii)

$f(x) = (2x+3) mod7\\ For \space any \space set \space A, the \space identity \space function \space A \space is \space not \space a \space bijection$