Question

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

Explanation:

Assuming the problem is to find \((f + g)(1)\) (the sum of the functions \(f\) and \(g\) evaluated at \(x = 1\)):

Step 1: Recall the sum of functions formula

The sum of two functions \(f(x)\) and \(g(x)\) is \((f + g)(x)=f(x)+g(x)\). So we first find \(f(1)\) and \(g(1)\) separately and then add them.

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

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

Step 3: Evaluate \(g(1)\)

Given \(g(x)=-3\sqrt[4]{x}-2\), substitute \(x = 1\):
Since \(\sqrt[4]{1}=1\), we have \(g(1)=-3(1)-2=-3 - 2=-5\).

Step 4: Find \((f + g)(1)\)

Using the sum of functions formula: \((f + g)(1)=f(1)+g(1)\). Substitute the values we found:
\((f + g)(1)=6+(-5)=6 - 5 = 1\).

Answer:

\(\boldsymbol{1}\)