Question

Given the equation g(x) = √x+1+3explain how to solve it and how to see if it's extraneous or not.

Answer 1

Solving the given equation,

`\begin{gathered} \sqrt[]{x+1}+3=0 \\ \sqrt[]{x+1}=-3 \\ (\sqrt[]{x+1})^2=(-3)^2 \\ x+1=9 \\ x=8 \end{gathered}`

Substituting the value of x in the original equation,

`\begin{gathered} g(x)=\sqrt[]{8+1}+3 \\ =\sqrt[]{9}+3 \\ =6\\e0 \end{gathered}`

Thus, x=8 is an extraneours solution.