Q58. - Algebra 2

Question

If $g\left(x\right)=x^2$, then $g\left(x+1\right)=$

$\text{A} 1.$     $\text{B} x^2+1.$              $\text{C} x^2+2x+1.$              \$[\text{D} x^2-x.\mathrm{\backslash ]}$

Step-by-Step Solution

Answer

The correct option is C

Step 1 – Perfect square formula

According to the perfect square trinomial or perfect square formula:

${\left(a+b\right)}^2=a^2+2ab+b^2$

 

Step 2 – Substitute the given value in the given function.

Substitute $x=x+1$ in the function $g\left(x\right)=x^2$.

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

Step 3 – Calculate the value by simplification.

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

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

If$g\left(x\right)=x^2$, then $g\left(x+1\right)=x^2+2x+1$.

Thus, the correct option is C.