Chapter 2: Q58. (page 62)

If $g (x) = x^{2}$ , then $g (x + 1) =$
$A 1 .$ $B x^{2} + 1 .$ $C x^{2} + 2 x + 1 .$ \ $[D x^{2} - x . \]$

Short Answer

Expert verified

The correct option is C

Step by step solution

– Perfect square formula

According to the perfect square trinomial or perfect square formula:

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

– Substitute the given value in the given function.

Substitute $x = x + 1$ in the function $g (x) = x^{2}$ .

$g (x + 1) = {(x + 1)}^{2}$

– Calculate the value by simplification.

The expression ${(x + 1)}^{2}$ is in the form of ${(a + b)}^{2}$ , where $a = x$ and $b = 1$ . Using the perfect square formula the function $g (x + 1) = {(x + 1)}^{2}$ can be written as:

$\begin{array}{l} g (x + 1) = {(x)}^{2} + 2 (x) (1) + {(1)}^{2} \\ g (x + 1) = x^{2} + 2 x + 1 \end{array}$

If $g (x) = x^{2}$ , then $g (x + 1) = x^{2} + 2 x + 1$ .

Thus, the correct option is C.

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If $g (x) = x^{2}$ , then $g (x + 1) =$
$A 1 .$ $B x^{2} + 1 .$ $C x^{2} + 2 x + 1 .$ \ $[D x^{2} - x . \]$

Short Answer

Step by step solution

– Perfect square formula

– Substitute the given value in the given function.

– Calculate the value by simplification.

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If g(x)=x2, then gx+1=A1. Bx2+1. Cx2+2x+1. \[Dx2-x.\]

Short Answer

Step by step solution

– Perfect square formula

– Substitute the given value in the given function.

– Calculate the value by simplification.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

If $g (x) = x^{2}$ , then $g (x + 1) =$
$A 1 .$ $B x^{2} + 1 .$ $C x^{2} + 2 x + 1 .$ \ $[D x^{2} - x . \]$