Question

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

Explanation:

Assuming we need to find \( f(1) \) and \( g(1) \) or maybe \( f(x)+g(x) \) at \( x = 1 \), let's solve for \( f(1) \) and \( g(1) \) first.

Step 1: Find \( f(1) \)

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

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

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

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

Step 3: Calculate \( f(1)+g(1) \)

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

If we want to find \( f(1)-g(1) \):
\( f(1)-g(1)=6-(-5)=6 + 5=11 \)

(The specific operation might depend on the actual question, but since the problem statement was a bit incomplete, we provided common operations like evaluating the functions at \( x = 1 \) and their sum/difference.)

Answer:

If evaluating \( f(1) \): \( \boldsymbol{6} \)

If evaluating \( g(1) \): \( \boldsymbol{-5} \)

If evaluating \( f(1)+g(1) \): \( \boldsymbol{1} \)

If evaluating \( f(1)-g(1) \): \( \boldsymbol{11} \)