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 \( x = 1 \) and maybe combine them (since the problem isn't fully stated, but common with such function setups is to find the sum or difference at \( x = 1 \); we'll proceed with evaluating each function at \( x = 1 \) first).

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

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

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

Substitute \( x = 1 \) into \( g(x)=-3\sqrt[4]{x}-2 \).
Again, \( \sqrt[4]{1}=1 \), so:
\( g(1)=-3\times\sqrt[4]{1}-2=-3\times1 - 2 \)
\( g(1)=-3 - 2=-5 \)

Step 3: (Optional, if finding \( f(1)+g(1) \))

Add the two results:
\( f(1)+g(1)=6+(-5)=1 \)

(If the problem was to find \( f(1)-g(1) \), it would be \( 6 - (-5)=11 \), but since the problem statement is partial, we'll assume the common case of sum or just evaluating each; here we show sum as a likely intent.)

Answer:

If evaluating \( f(1)+g(1) \), the answer is \( \boldsymbol{1} \).
(If the problem was different, adjust based on full context, but with given info, this is a common solution path.)