Question

26 a) f(x) = (3x - 15)/(2x + 12)

Explanation:

Assuming we need to find the domain, vertical asymptote, or simplify the function. Let's simplify first.

Step1: Factor numerator and denominator

Numerator: \(3x - 15 = 3(x - 5)\)
Denominator: \(2x + 12 = 2(x + 6)\)
So \(f(x)=\frac{3(x - 5)}{2(x + 6)}\)

Step2: Analyze domain (if needed)

Denominator cannot be zero: \(2(x + 6)
eq0\Rightarrow x
eq - 6\)

Step3: Vertical asymptote (if needed)

Vertical asymptote at \(x=-6\) (since denominator is zero here and numerator is non - zero at \(x = - 6\))

(If the question was different, like finding horizontal asymptote:
Degree of numerator and denominator is 1. Horizontal asymptote is \(\frac{3}{2}\))

Answer:

Simplified: \(\boldsymbol{f(x)=\frac{3(x - 5)}{2(x + 6)}}\), Domain: \(x
eq - 6\), Vertical Asymptote: \(x=-6\) (depending on the exact question, adjust the answer)