Question

show the function f: r➡️r. defined f(x)=1/x is one one and onto

Answer 1

hello friend..!!

according to the question we should show the function, 1 / x is one - one and onto.

1) to prove it is one - one :

let. f( x1 ) = f(x2)

implies, 1 / x1 = 1 / x2

implies, x2 = x1 --------------( 1. )

implies, x1. = x2

therefore, f ( x) is one - one function.

2) to prove it is an onto function :

let, y = 1 / x

implies, x = 1 / y

for all y € R, there exist at least one X in R such that,

f( x) = f ( 1 / y)

= 1 / ( 1/y)

= y.

therefore f( x) is onto function.

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hope it helps..!!!