Operations (1) Let $$ f(x)=5 \sqrt{x} $$ and $$ g(x)=-8 \sqrt{x} $$ Find $$ (f+g)(x) $$ and $$ (F-g)(x) $$ State domain of each Then evaluate $$ (f+g) $$ and $$ (f-g) $$ for the $$ x=16 $$. (a) $$ (f+g)(16)= $$ Step $$ 8-1 \quad f(x)+g(x) $$ $$ 5 \sqrt{16}+(-8 \sqrt{x}) $$ Step:-2 $$ 5 \sqrt{16}-8 \sqrt{x} $$ $$ 5-8 \sqrt{x} \rightarrow-3 \sqrt{x} $$ Step: 3 Let $$ x=16 $$ $$ \begin{array}{c} -3 \sqrt{16} \ -3(4) \ -12) \end{array} $$ Step: 4 Domain: $$ x \geq 0 $$

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**Step 1.** Write the functions:
$$
f(x)=5\sqrt{x}, \quad g(x)=-8\sqrt{x}.
$$

**Step 2.** Find $$(f+g)(x)$$:
$$
(f+g)(x) = f(x) + g(x)= 5\sqrt{x} + (-8\sqrt{x}) = (5-8)\sqrt{x} = -3\sqrt{x}.
$$
The domain is determined by the square root, so $$\text{Domain: } x\geq 0$$.

**Step 3.** Find $$(f-g)(x)$$:
$$
(f-g)(x) = f(x) - g(x)= 5\sqrt{x} - (-8\sqrt{x}) = 5\sqrt{x} + 8\sqrt{x} = 13\sqrt{x}.
$$
The domain is also $$x\geq 0$$.

**Step 4.** Evaluate $$(f+g)(16)$$:
$$
(f+g)(16) = -3\sqrt{16} = -3(4) = -12.
$$

**Step 5.** Evaluate $$(f-g)(16)$$:
$$
(f-g)(16) = 13\sqrt{16} = 13(4) = 52.
$$
$$ (f+g)(16) = -12 \quad \text{and} \quad (f-g)(16) = 52 $$

Operations
(1) Let and

Find and
State domain of each
Then evaluate and for the .
(a)

Step

Step:-2

Step: 3 Let

Step: 4 Domain:

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Operations (1) Let and Find and State domain of each Then evaluate and for the . (a) Step Step:-2 Step: 3 Let Step: 4 Domain: