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

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

[tex]\[
\text{Answer here:} \quad \_\_\_\_\_\_\_
\][/tex]

Sagot :

Let's find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex].

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

2. Calculate [tex]\( 2(2)^2 \)[/tex]:
[tex]\[ 2(2)^2 = 2 \cdot 4 = 8 \][/tex]

3. Next, calculate [tex]\( 5\sqrt{2+2} \)[/tex]:
[tex]\[ 5\sqrt{2+2} = 5\sqrt{4} = 5 \cdot 2 = 10 \][/tex]

4. Now, add these two results together:
[tex]\[ f(2) = 8 + 10 = 18 \][/tex]

So, the answer is
[tex]\[ f(2) = 18 \][/tex]