Injective or Surjective - AQ1.9: Activity Questions 9 Q.3

[Mukul Kr Singh Chauhan]

Why the following function is not Injective

Let f:R→R be a function and f(x)=|(x+4)(4x−10)|.

When I did f(x1) = f(x2) it gave me x1 = x2.

Can someone please explain this.

Thanks in advance.

Regards,

[Sanskar Rajput]

for different elements in the domain ,if function has same value then function is not injective 

in this example ,for value x = -4 and x = 2.5 function value is zero , so this function is not injective

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[Mukul Kr Singh Chauhan]

I applied the Injective fn theorem which states f(x1) = f(x2) that gave me x1 = x2 and hence concluded Injective but the answer says it is not. This is where the confusion arises.

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[Mukul Kr Singh Chauhan]

Resolved. However is it possible for a Fn to be subjective without being Injective???

[Sanskar Rajput]

you also try this ,

https://en.wikipedia.org/wiki/Injective_function

best clarification .

[Mukul Kr Singh Chauhan]

Thanks, I will check it out