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:

$\lbrack-6,\infty)$