Question

show that the function f(X) = 3x + 2 is one - one and onto

Answer 1

hello friend...!!!

according to the question we should prove f(x) is one - one and onto,

1) to prove it is one - one :

let, f(x1) = f(x2)

implies, 3x1 +2 = 3x2 + 2

implies, x1 = x2

therefore it is one - one function.

2) to prove it is onto function :

let y = 3x + 2

implies, x= y - 2 / 3

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

f ( x) = f ( y - 2 / 3 )

= 3 ( y - 2 / 3 ) + 2

= y -2 +2

= y .

therefore f( x) is onto function.

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hope it helps....!!!!