Answer:
[tex]\textsf{(d)} \quad \boxed{9a+9h-3}[/tex]
[tex]\textsf{(e)} \quad \boxed{9a+9h-6}[/tex]
[tex]\textsf{(f)} \quad \boxed{9}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x) = 9x - 3[/tex]
Part (d)
To find f(a + h), substitute x = a + h into the function:
[tex]\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}[/tex]
Part (e)
Find f(a) by substituting x = a into the function:
[tex]\implies f(a)=9a-3[/tex]
Find f(h) by substituting x = h into the function:
[tex]\implies f(h)=9h-3[/tex]
Therefore:
[tex]\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}[/tex]
Part (f)
[tex]\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}[/tex]
