To find [tex]\( f(8) \)[/tex] for the function [tex]\( f(x) = -\frac{26}{x+7} \)[/tex], we need to substitute [tex]\( x = 8 \)[/tex] into the function and then simplify.
Here's the step-by-step solution:
1. Start with the formula for the function:
[tex]\[ f(x) = -\frac{26}{x+7} \][/tex]
2. Substitute [tex]\( x = 8 \)[/tex] into the function:
[tex]\[ f(8) = -\frac{26}{8+7} \][/tex]
3. Simplify the expression inside the denominator:
[tex]\[ 8 + 7 = 15 \][/tex]
4. Now substitute back into the fraction:
[tex]\[ f(8) = -\frac{26}{15} \][/tex]
Therefore, the value of [tex]\( f(8) \)[/tex] is:
[tex]\[ -\frac{26}{15} \][/tex]
Comparing with the options provided:
- (A) [tex]\( -\frac{26}{15} \)[/tex]
- (B) [tex]\( -\frac{13}{4} \)[/tex]
- (C) [tex]\( -\frac{4}{13} \)[/tex]
- (D) [tex]\( -\frac{15}{26} \)[/tex]
The correct answer is [tex]\(\boxed{-\frac{26}{15}}\)[/tex].
