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Chapter 2: Q58. (page 62)

If g(x)=x2, then gx+1=

A1. Bx2+1. Cx2+2x+1. \[Dx2-x.\]

Short Answer

Expert verified

The correct option is C

Step by step solution

01

– Perfect square formula

According to the perfect square trinomial or perfect square formula:

a+b2=a2+2ab+b2

02

– Substitute the given value in the given function.

Substitute x=x+1in the function gx=x2.

gx+1=x+12

03

– Calculate the value by simplification.

The expression x+12is in the form of a+b2, where a=xand b=1. Using the perfect square formula the function gx+1=x+12can be written as:

gx+1=x2+2x1+12gx+1=x2+2x+1

Ifgx=x2, then gx+1=x2+2x+1.

Thus, the correct option is C.

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