Question

the function h is defined by h(x) = (7 + x)/(-6 + 3x). find h(n - 3). h(n - 3) =

Explanation:

Step1: Substitute \( x = n - 3 \) into \( h(x) \)

We have \( h(x)=\frac{7 + x}{-6 + 3x} \), so substitute \( x=n - 3 \) into the function:
\( h(n - 3)=\frac{7+(n - 3)}{-6+3(n - 3)} \)

Step2: Simplify the numerator and denominator

• Simplify the numerator: \( 7+(n - 3)=7 + n-3=n + 4 \)
• Simplify the denominator: \( -6+3(n - 3)=-6 + 3n-9=3n-15 \)

So \( h(n - 3)=\frac{n + 4}{3n-15} \) (we can also factor the denominator as \( 3(n - 5) \), but the simplified form with numerator \( n + 4 \) and denominator \( 3n-15 \) is also correct)

Answer:

\( \frac{n + 4}{3n - 15} \) (or \( \frac{n + 4}{3(n - 5)} \))