If [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex], complete the following statement:

[tex]\( f(2) = \)[/tex] \_\_\_\_\_

Answer here: 7.05



Answer :

To solve for [tex]\( f(2) \)[/tex] when given the function [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex], follow these steps:

1. Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(2) = 2(2)^2 + 5\sqrt{2 + 2} \][/tex]

2. Evaluate the squared term [tex]\( (2)^2 \)[/tex]:
[tex]\[ (2)^2 = 4 \][/tex]

3. Multiply the squared term by the coefficient 2:
[tex]\[ 2 \times 4 = 8 \][/tex]

4. Substitute [tex]\( x = 2 \)[/tex] into the square root term [tex]\( \sqrt{(2 + 2)} \)[/tex]:
[tex]\[ \sqrt{2 + 2} = \sqrt{4} \][/tex]

5. Evaluate the square root [tex]\( \sqrt{4} \)[/tex]:
[tex]\[ \sqrt{4} = 2 \][/tex]

6. Multiply the square root term by the coefficient 5:
[tex]\[ 5 \times 2 = 10 \][/tex]

7. Add the results of the two terms together:
[tex]\[ 8 + 10 = 18 \][/tex]

Therefore, the value of [tex]\( f(2) \)[/tex] is [tex]\( 18 \)[/tex]. [tex]\( f(2) = 18 \)[/tex]