Sure, let's find the value of [tex]\( f\left(\frac{1}{3}\right) \)[/tex] for the function [tex]\( f(x) = 18x^2 + 30x + 2 \)[/tex].
1. Substitute [tex]\( x = \frac{1}{3} \)[/tex] into the function:
[tex]\[
f\left(\frac{1}{3}\right) = 18 \left(\frac{1}{3}\right)^2 + 30 \left(\frac{1}{3}\right) + 2
\][/tex]
2. Calculate [tex]\( \left(\frac{1}{3}\right)^2 \)[/tex]:
[tex]\[
\left(\frac{1}{3}\right)^2 = \frac{1}{9}
\][/tex]
3. Multiply 18 by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[
18 \times \frac{1}{9} = 2
\][/tex]
4. Multiply 30 by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[
30 \times \frac{1}{3} = 10
\][/tex]
5. Add the results together:
[tex]\[
f\left(\frac{1}{3}\right) = 2 + 10 + 2
\][/tex]
[tex]\[
f\left(\frac{1}{3}\right) = 14
\][/tex]
So, the value of [tex]\( f\left(\frac{1}{3}\right) \)[/tex] is:
[tex]\[
f\left(\frac{1}{3}\right) = 14
\][/tex]
