Question

If f:R->Ris defined as f (x)=2x2-1,find the pre -images of 17,4and-2

Answer 1

Step-by-step explanation:

For pre image of 17 we have:

f(x)=x

2

+1=17

⇒x

2

+1=17

⇒x

2

=16

⇒x=

16

⇒x=±4

So, x∈{−4,4}

For pre image of −3 we have:

f(x)=x

2

+1=−3

⇒x

2

+1=−3

⇒x

2

=−4 (NOT possible)

Hennce, no possible pre image.

So, x∈ϕ