Answer :
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]
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]
