Question

1. $f(x) = 5sqrt4{x} + 1, g(x) = -3sqrt4{x} - 2; x = 1$

Explanation:

Assuming we need to find \( f(1) + g(1) \) or evaluate the functions at \( x = 1 \), here's the step - by - step solution:

Step 1: Evaluate \( f(1) \)

Given \( f(x)=5\sqrt[4]{x}+1 \), substitute \( x = 1 \) into the function. Since \( \sqrt[4]{1}=1 \) (because \( 1^4 = 1 \)), we have:
\( f(1)=5\times\sqrt[4]{1}+1=5\times1 + 1=5 + 1 = 6 \)

Step 2: Evaluate \( g(1) \)

Given \( g(x)=- 3\sqrt[4]{x}-2 \), substitute \( x = 1 \) into the function. Since \( \sqrt[4]{1}=1 \), we get:
\( g(1)=-3\times\sqrt[4]{1}-2=-3\times1-2=-3 - 2=-5 \)

Step 3: (Optional) If we want to find \( f(1)+g(1) \)

Add the values of \( f(1) \) and \( g(1) \) together:
\( f(1)+g(1)=6+(-5)=6 - 5 = 1 \)

If the question was to evaluate \( f(1) \), the answer is \( 6 \); if it was to evaluate \( g(1) \), the answer is \( - 5 \); if it was to find \( f(1)+g(1) \), the answer is \( 1 \). Since the original problem was not fully specified (maybe to evaluate the functions at \( x = 1 \) and perhaps add them), we'll assume the most common case of finding \( f(1)+g(1) \).

Answer:

\( 1 \)