To find [tex]\( f(4) \)[/tex] for the function [tex]\( f(s) = \frac{7s - 12}{2s - 14} \)[/tex], follow these steps:
1. Substitute [tex]\( s = 4 \)[/tex] into the function:
[tex]\[ f(4) = \frac{7(4) - 12}{2(4) - 14} \][/tex]
2. Calculate the numerator and the denominator separately:
- For the numerator:
[tex]\[ 7(4) - 12 = 28 - 12 = 16 \][/tex]
- For the denominator:
[tex]\[ 2(4) - 14 = 8 - 14 = -6 \][/tex]
3. Combine them into the fraction:
[tex]\[ f(4) = \frac{16}{-6} \][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{16}{-6}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{16 \div 2}{-6 \div 2} = \frac{8}{-3} = -\frac{8}{3} \][/tex]
So, the value of [tex]\( f(4) \)[/tex] is:
[tex]\[ f(4) = -\frac{8}{3} \][/tex]
In decimal form, [tex]\(-\frac{8}{3}\)[/tex] is approximately [tex]\(-2.6666666666666665\)[/tex].
Therefore,
[tex]\[ f(4) = -2.6666666666666665 \][/tex]
This is the simplified result for the function [tex]\( f \)[/tex] at [tex]\( s = 4 \)[/tex].
