Question

Determine which of the value(s), if any, must be excluded from the domain of the variable in the expression x^2/x^2+25 x=3, x=5, x=0, x=-5

Answer 1

Given

$\frac{x^2}{x^2+25}$

The values of x for which x must be excluded from the domain of the variable in the expression is the values of x for which the expression is undefined. The expression is undefined when the denominator is equal to zero as shown below

$x^2+25=0$

Let us solve for x

$\begin{gathered} x^2+25=0 \\ x^2=-25 \end{gathered}$$\begin{gathered} \text{taking square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{-25} \\ x=\sqrt[]{-1}\times\sqrt[]{25} \\ \sqrt[]{-1}=i,\sqrt[]{25}=\pm5 \\ x=\pm5i \end{gathered}$

Hence, the value of x that must be excluded from the domain of the variable in the expression is +5i and -5i