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 functions is to evaluate at \( x = 1 \) and perhaps add or find a combination). Let's 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:
\( f(1) = 5\sqrt[4]{1} + 1 = 5(1) + 1 = 5 + 1 = 6 \)

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

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

Step 3: If we need \( f(1) + g(1) \) (a common operation with two functions at a point)

Add the results from Step 1 and Step 2:
\( f(1) + g(1) = 6 + (-5) = 1 \)

(If the problem was to find \( f(1) - g(1) \) or another operation, adjust accordingly, but since it's not specified, but the most common is sum or just evaluating each. However, let's check the arithmetic again.)

Wait, maybe the problem is to find \( (f + g)(1) \), which is \( f(1) + g(1) \). Let's confirm:

\( f(1) = 5\sqrt[4]{1} + 1 = 5(1) + 1 = 6 \)

\( g(1) = -3\sqrt[4]{1} - 2 = -3(1) - 2 = -5 \)

Then \( f(1) + g(1) = 6 + (-5) = 1 \). Alternatively, if we consider \( (f - g)(1) \), it would be \( 6 - (-5) = 11 \), but since the problem statement is cut off, but given the functions, evaluating at \( x = 1 \) and combining is likely.

Alternatively, maybe the problem is to find \( f(1) \) and \( g(1) \) separately. Let's present both:

\( f(1) = 6 \), \( g(1) = -5 \), and if we add them, \( 1 \).

Answer:

If we assume the problem is to find \( f(1) + g(1) \), the answer is \( \boldsymbol{1} \). If it's to find \( f(1) \), it's \( 6 \); for \( g(1) \), it's \( -5 \). Based on common problems with two functions and a value of \( x \), the combined result (sum) is \( 1 \).