Certainly! Let's solve for [tex]\(f(x)\)[/tex] when [tex]\(x = 4\)[/tex] using the given function [tex]\( f(x) = \sqrt{2x - 1} \)[/tex].
### Step-by-Step Solution:
1. Identify the function:
The function given is:
[tex]\[
f(x) = \sqrt{2x - 1}
\][/tex]
2. Substitute the value of [tex]\( x \)[/tex] into the function:
We need to find [tex]\( f(4) \)[/tex]. This means we substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
f(4) = \sqrt{2 \cdot 4 - 1}
\][/tex]
3. Simplify inside the square root:
Perform the arithmetic inside the square root:
[tex]\[
2 \cdot 4 = 8
\][/tex]
[tex]\[
8 - 1 = 7
\][/tex]
4. Evaluate the square root:
Now we need to find the square root of 7:
[tex]\[
\sqrt{7}
\][/tex]
5. Find the decimal approximation:
By looking it up or using a calculator, the square root of 7 is approximately:
[tex]\[
\sqrt{7} \approx 2.6457513110645907
\][/tex]
### Conclusion:
Thus, the value of [tex]\( f(4) \)[/tex] is:
[tex]\[
f(4) \approx 2.6457513110645907
\][/tex]
This is the result when you evaluate the function [tex]\( f(x) = \sqrt{2x - 1} \)[/tex] at [tex]\( x = 4 \)[/tex].
