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 eack Then evaluate $$ (f+g) $$ and $$ (f-g) $$ for the $$ x=16 $$. (a) $$ (f+g)(16)= $$ Step :-1 $$ \quad f_{x}+g x $$ $$ 5 \sqrt{16}+(-8 \sqrt{16}) $$ Step:-2 $$ 5 \sqrt{16}-8 \sqrt{16} $$ $$ 5 - 8 \longdiv { 1 6 } $$ Step:3 $$ -3 \sqrt{16} $$ $$ -3(4) $$ Step:4 -12 Step:S Domain: $$ x \geq 0 $$

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Let's solve the problem step by step.

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

2. **Find $$ (f+g)(x) $$ and $$ (f-g)(x) $$:**
   - $$ (f+g)(x) = f(x) + g(x) = 5 \sqrt{x} - 8 \sqrt{x} = -3 \sqrt{x} $$
   - $$ (f-g)(x) = f(x) - g(x) = 5 \sqrt{x} - (-8 \sqrt{x}) = 5 \sqrt{x} + 8 \sqrt{x} = 13 \sqrt{x} $$

3. **State the domain:**
   - The domain for both functions is $$ x \geq 0 $$ since the square root function is defined for non-negative values.

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

- For $$ (f-g)(16) $$:
     $$
     (f-g)(16) = 13 \sqrt{16}
     $$
     $$
     = 13(4) = 52
     $$

### Summary of Results:
- $$ (f+g)(16) = -12 $$
- $$ (f-g)(16) = 52 $$
- Domain: $$ x \geq 0 $$
$$ (f+g)(16) = -12 $$ and $$ (f-g)(16) = 52 $$. The domain for both functions is $$ x \geq 0 $$.

Operations
(1) Let and

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

Step :-1

Step:-2

Step:3

Step:4 -12
Step:S Domain:

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Operations (1) Let and Find and State domain of eack Then evaluate and for the . (a) Step :-1 Step:-2 Step:3 Step:4 -12 Step:S Domain: