Given [tex]$f(x)=\sqrt[3]{4x+3}$[/tex], find [tex][tex]$f(3.2)$[/tex][/tex]. Your answer should be written in decimal notation, rounded to 4 decimal places.
### 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]
