If :R → R is defined as f(x) Solution: To find the pre-image of 17, we solve the counti 2x² 1, find the pre-images of 17,4 and -2.
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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
Answered by
6
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