Question

Hello what is the answer to this and the domain

Answer 1

We are given the following functions:

`\begin{gathered} f(x)=7\sqrt[]{x}+6 \\ g(x)=x+6 \end{gathered}`

We are asked to determine the composite function:

`(f\circ g)(x)`

The composition of functions is equivalent to:

`(f\circ g)(x)=f(g(x))`

Therefore, we replace the value of "x" in function "f" for the function "g", therefore, we get:

`(f\circ g)(x)=f(g(x))=7\sqrt[]{x+6}+6`

Since we can't simplify any further this is the composition.

Now we are asked to determine the domain of this function. Since we have a square root, the domain must be the values of "x" where the term inside the radical is greater or equal to zero, therefore, we have:

`x+6\ge0`

Now we solve for "x" by subtracting 6 from both sides:

`x\ge-6`

Therefore, the domain is:

`\lbrack-6,\infty)`