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

[tex]\( f(0) = \)[/tex]

Sagot :

GinnyAnswer
Let's find [tex]\(f(0)\)[/tex] for the function [tex]\(f(x) = 2(x)^2 + 5 \sqrt{(x+2)}\)[/tex].

1. Firstly, substitute [tex]\(x = 0\)[/tex] into the function:
[tex]\[ f(0) = 2(0)^2 + 5 \sqrt{(0 + 2)} \][/tex]

2. Simplify the expression:
[tex]\[ f(0) = 2 \cdot 0^2 + 5 \sqrt{2} \][/tex]

3. Recognize that [tex]\(0^2\)[/tex] is 0:
[tex]\[ 2 \cdot 0^2 = 0 \][/tex]
and thus:
[tex]\[ f(0) = 0 + 5 \sqrt{2} \][/tex]

4. Finally, calculate [tex]\(5 \sqrt{2}\)[/tex]. The value of [tex]\(\sqrt{2}\)[/tex] is approximately 1.414. Therefore:
[tex]\[ 5 \sqrt{2} \approx 5 \times 1.414 = 7.07 \][/tex]

So, [tex]\(f(0) = 7.07\)[/tex] when rounded to the nearest hundredth.

Therefore, the completed statement is:
[tex]\[ f(0) = 7.07 \][/tex]
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