To determine [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = 2x^2 + 5\sqrt{x-2} \)[/tex], let's follow a step-by-step process.
1. Begin by substituting [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
[tex]\[
f(x) = 2x^2 + 5\sqrt{x-2}
\][/tex]
[tex]\[
f(3) = 2(3)^2 + 5\sqrt{3-2}
\][/tex]
2. Calculate the value of [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply this result by 2:
[tex]\[
2 \cdot 9 = 18
\][/tex]
4. Next, compute the inside of the square root [tex]\( 3 - 2 \)[/tex]:
[tex]\[
3 - 2 = 1
\][/tex]
5. Find the square root of 1:
[tex]\[
\sqrt{1} = 1
\][/tex]
6. Multiply this result by 5:
[tex]\[
5 \cdot 1 = 5
\][/tex]
7. Finally, add the two parts together:
[tex]\[
18 + 5 = 23
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is:
[tex]\[
f(3) = 23.0
\][/tex]
So, the completed statement is:
[tex]\[
f(3) = 23.0
\][/tex]
