Question

Given f(x) = √x²+4 and g(x)= 2x+1 . Find the domain of f(x)/g(x)

Answer 1

gIven:

`\begin{gathered} \: f\mleft(x\mright)\: =\: \sqrt[]{x^2+4} \\ g\mleft(x\mright)=-\: 2x+1 \end{gathered}`

Find the domain of

`(f\left(x\right))/(g\left(x\right))`

to solve,

`(f\left(x\right))/(g\left(x\right))=(√(x^2+4))/(-2x+1)`

The domain of the above function is,

The undefined points are,

`\begin{gathered} x<(1)/(2) \\ \: x>(1)/(2) \end{gathered}`

the answer is

In interval notation,

`(-\infty\: ,\: (1)/(2))\cup((1)/(2),\: \infty\: )`