Questions: f(x) = (x^5 + 2) / 4

Transcript text: 3. $f(x)=\frac{x^{5}+2}{4}$

Solution

Solution Steps

To evaluate the function $ f(x) = \frac{x^5 + 2}{4} $ for a given value of $ x $, we need to substitute the value of $ x $ into the function and perform the arithmetic operations.

Step 1: Define the Function

The function given is: \[ f(x) = \frac{x^5 + 2}{4} \]

Step 2: Substitute $ x = 2 $ into the Function

We substitute $ x = 2 $ into the function: \[ f(2) = \frac{2^5 + 2}{4} \]

Step 3: Calculate the Exponent

Calculate $ 2^5 $: \[ 2^5 = 32 \]

Step 4: Add 2 to the Result

Add 2 to the result of the exponentiation: \[ 32 + 2 = 34 \]

Step 5: Divide by 4

Divide the result by 4: \[ \frac{34}{4} = 8.5 \]

Final Answer

\[\boxed{f(2) = \frac{17}{2}}\]

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