Answer :
To find the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 2 \)[/tex], follow these steps:
1. Start with the given function:
[tex]\[ f(x) = 2(x^2) + 5\sqrt{x + 2} \][/tex]
2. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 2(2^2) + 5\sqrt{2 + 2} \][/tex]
3. Calculate [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
4. Substitute this result back into the equation:
[tex]\[ f(2) = 2(4) + 5\sqrt{4} \][/tex]
5. Calculate [tex]\( 2(4) \)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
6. Simplify the square root of [tex]\( 4 \)[/tex]:
[tex]\[ \sqrt{4} = 2 \][/tex]
7. Substitute the result of the square root into the equation:
[tex]\[ f(2) = 8 + 5(2) \][/tex]
8. Calculate [tex]\( 5 \cdot 2 \)[/tex]:
[tex]\[ 5 \cdot 2 = 10 \][/tex]
9. Add the results:
[tex]\[ 8 + 10 = 18 \][/tex]
Thus, the value of the function when [tex]\( x = 2 \)[/tex] is:
[tex]\[ f(2) = 18 \][/tex]
1. Start with the given function:
[tex]\[ f(x) = 2(x^2) + 5\sqrt{x + 2} \][/tex]
2. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 2(2^2) + 5\sqrt{2 + 2} \][/tex]
3. Calculate [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
4. Substitute this result back into the equation:
[tex]\[ f(2) = 2(4) + 5\sqrt{4} \][/tex]
5. Calculate [tex]\( 2(4) \)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
6. Simplify the square root of [tex]\( 4 \)[/tex]:
[tex]\[ \sqrt{4} = 2 \][/tex]
7. Substitute the result of the square root into the equation:
[tex]\[ f(2) = 8 + 5(2) \][/tex]
8. Calculate [tex]\( 5 \cdot 2 \)[/tex]:
[tex]\[ 5 \cdot 2 = 10 \][/tex]
9. Add the results:
[tex]\[ 8 + 10 = 18 \][/tex]
Thus, the value of the function when [tex]\( x = 2 \)[/tex] is:
[tex]\[ f(2) = 18 \][/tex]
