Sure, let's evaluate the function [tex]\( f(x) = \sqrt[3]{2x + 9} \)[/tex] for the given values step-by-step:
### Part (a): [tex]\( f(9) \)[/tex]
We need to find [tex]\( f(9) \)[/tex].
[tex]\[ f(x) = \sqrt[3]{2x + 9} \][/tex]
So,
[tex]\[ f(9) = \sqrt[3]{2 \cdot 9 + 9} \][/tex]
[tex]\[ f(9) = \sqrt[3]{18 + 9} \][/tex]
[tex]\[ f(9) = \sqrt[3]{27} \][/tex]
The cube root of 27 is:
[tex]\[ \sqrt[3]{27} = 3 \][/tex]
Therefore,
[tex]\[ f(9) = 3.00 \][/tex]
### Part (b): [tex]\( f(20) \)[/tex]
We need to find [tex]\( f(20) \)[/tex].
[tex]\[ f(x) = \sqrt[3]{2x + 9} \][/tex]
So,
[tex]\[ f(20) = \sqrt[3]{2 \cdot 20 + 9} \][/tex]
[tex]\[ f(20) = \sqrt[3]{40 + 9} \][/tex]
[tex]\[ f(20) = \sqrt[3]{49} \][/tex]
The cube root of 49, rounded to two decimal places, is approximately:
[tex]\[ \sqrt[3]{49} \approx 3.66 \][/tex]
Therefore,
[tex]\[ f(20) = 3.66 \][/tex]
So, the evaluated values are:
a) [tex]\( f(9) = 3.00 \)[/tex]
b) [tex]\( f(20) = 3.66 \)[/tex]
