Question

Compute the domains off and g. Give your answers in interval notation. (Hint: It mayhelp to rewrite each function in radical notation first and then refer to question 4)f(x) = (x + 10)g(x) = (x + 10)¹/3

Answer 1

Given

`\begin{gathered} f(x)=(x+10)^{(1)/(2)} \\ \\ g(x)=(x+10)^{(1)/(3)} \end{gathered}`

Find

Domain of the function

Step-by-step explanation

Domain of the function is the set of all possible values of x which will given the output value y.

`\begin{gathered} f(x)=√((x+10)) \\ x+10=0 \\ x=-10 \end{gathered}`

so , domain of the function , f(x) =

`[-10,\infty)`

and

as we know that the domain of the function is all real numbers except where the function is undefined.

in this case , there is no real number which makes the function undefined.

so , domain of g(x) is all values of x

so ,

`g(x)=(-\infty,\infty)`

Final Answer

Therefore , the domain of f(x) anf g(x) are

`f(x)=[-10,\infty)`
`g(x)=(-\infty,\infty)`