Question

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

Explanation:

Assuming we need to find the domain of \( f(x)=\frac{3x - 15}{2x+12} \) (a common problem with rational functions).

Step1: Identify the denominator

The denominator of the function is \( 2x + 12 \).

Step2: Set denominator not equal to zero

For the function to be defined, the denominator cannot be zero. So we solve \( 2x+12
eq0 \).
Subtract 12 from both sides: \( 2x
eq - 12 \).
Divide both sides by 2: \( x
eq - 6 \).
So the domain is all real numbers except \( x = - 6 \), or in interval notation \( (-\infty,-6)\cup(-6,\infty) \). (If the problem was different, like simplifying, we could factor numerator and denominator: numerator \( 3(x - 5) \), denominator \( 2(x + 6) \), so simplified form is \( \frac{3(x - 5)}{2(x + 6)} \) for \( x
eq - 6 \))

Answer:

If finding domain: All real numbers except \( x=-6 \) (or \( (-\infty, - 6)\cup(-6, \infty) \)); If simplifying: \( \frac{3(x - 5)}{2(x + 6)} \) (\( x
eq - 6 \))