​Given function f, prove that f(x)=4-2x is a one -to-one function.

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Given function f, prove that f(x)=4-2x is a one -to-one function.

Apr 26th, 2015

A one-to-one function is a function for which every element of the range of the function corresponds to exactly one element of the domain.


f(x) = 4 - 2x

We have to show that 

if f(x1)=f(x2), then x1=x2

In other words we have to show that for each value of y there exists only a unique value of x.

f(x1)=f(x2)
4 - 2x1  = 4 - 2x2
-2x1 = 4 - 2x2 - 4
-2x1 = -2x2
x1 = x2

Hence f(x) = 4 - 2x is a one-to-one function.

NOTE: In x1 and  x2 , 1 and 2 are subscripts
Apr 26th, 2015

Thank you.

May 2nd, 2015

Happy to help :)

May 2nd, 2015

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Apr 26th, 2015
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