To solve for [tex]\( f(x) = \sqrt{x^2 + x} \)[/tex] at a specific value of [tex]\( x \)[/tex], follow these steps:
1. Substitute the value of [tex]\( x \)[/tex] into the function:
First, we need to choose a value for [tex]\( x \)[/tex]. Let's use [tex]\( x = 5 \)[/tex].
[tex]\[
f(5) = \sqrt{5^2 + 5}
\][/tex]
2. Calculate the expression inside the square root:
Compute [tex]\( 5^2 + 5 \)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
Adding 5 to 25:
[tex]\[
25 + 5 = 30
\][/tex]
3. Simplify the square root expression:
Now take the square root of 30:
[tex]\[
f(5) = \sqrt{30}
\][/tex]
4. Determine the square root value:
The square root of 30 is approximately [tex]\( 5.477225575051661 \)[/tex].
Therefore, [tex]\( f(x) \)[/tex] at [tex]\( x = 5 \)[/tex] is:
[tex]\[
f(5) = 5.477225575051661
\][/tex]
This detailed step-by-step evaluation shows that [tex]\( f(5) = 5.477225575051661 \)[/tex].
