To find [tex]\( f(3.2) \)[/tex] for the function [tex]\( f(x) = \sqrt[3]{4x + 3} \)[/tex], we will follow these steps:
1. Substitute [tex]\( x = 3.2 \)[/tex] into the function [tex]\( f(x) \)[/tex].
2. Calculate the expression inside the cube root.
3. Evaluate the cube root.
4. Round the final result to 4 decimal places.
Let’s go through each of these steps in detail:
### Step 1: Substitute [tex]\( x = 3.2 \)[/tex]
[tex]\[
f(3.2) = \sqrt[3]{4 \cdot 3.2 + 3}
\][/tex]
### Step 2: Calculate the expression inside the cube root
First, we need to calculate [tex]\( 4 \cdot 3.2 \)[/tex]:
[tex]\[
4 \cdot 3.2 = 12.8
\][/tex]
Next, add 3 to this result:
[tex]\[
12.8 + 3 = 15.8
\][/tex]
So the expression inside the cube root becomes [tex]\( 15.8 \)[/tex].
### Step 3: Evaluate the cube root
Now, we need to compute the cube root of [tex]\( 15.8 \)[/tex]:
[tex]\[
\sqrt[3]{15.8}
\][/tex]
### Step 4: Round the final result to 4 decimal places
After calculating [tex]\( \sqrt[3]{15.8} \)[/tex], the result is approximately 2.5093 when rounded to 4 decimal places.
Therefore, the value of [tex]\( f(3.2) \)[/tex] is:
[tex]\[
f(3.2) \approx 2.5093
\][/tex]
