Solution to Define a bijective function. Explain with reasons whether the following functions are bijective or not. … - Sikademy
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Archangel Macsika

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

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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

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