Question

refer to the functions defined below.
$f(x)=x + 3$\t$h(x)=x^2 + 6$
find the indicated function and simplify if possible.
part: 0 / 2
part 1 of 2
$(f + h)(x)=\boxed{x^2 + x + 9}$
part: 1 / 2
part 2 of 2
list any domain restrictions of $(f + h)(x)$. if there is more than one restriction for the variable, use the \and\ button. select
one\ if appropriate.
domain restrictions: $x\
eq\square$.

Explanation:

Step1: Analyze the function \((f + h)(x)\)

We know that \(f(x)=x + 3\) and \(h(x)=x^{2}+6\). Then \((f + h)(x)=f(x)+h(x)=(x + 3)+(x^{2}+6)=x^{2}+x + 9\). This is a polynomial function.

Step2: Determine the domain of a polynomial function

The domain of a polynomial function (like quadratic, linear, cubic etc.) is all real numbers because there are no values of \(x\) for which the function is undefined (no division by zero, no square roots of negative numbers in the case of a polynomial with real coefficients). So there are no domain restrictions.

Answer:

None