f(x)=6x-9 find [f(a+h)-f(a)]/h
You asked:
Evaluate the function \(f\left( x \right) = 6 x - 9\), \(\frac{f\left( a + h \right) - f\left( a \right)}{h}\).
MathBot Answer:
$$\begin{aligned}\frac{f\left( a + h \right) - f\left( a \right)}{h}&=6\end{aligned}$$
$$\begin{aligned}\frac{f\left( a + h \right) - f\left( a \right)}{h}&=\frac{-\left(-9 + 6 a\right) + -9 + 6 \left(a + h\right)}{h}\\\frac{f\left( a + h \right) - f\left( a \right)}{h}&=\frac{-9 + 6 \left(a + h\right) + 9 - 6 a}{h}\\\frac{f\left( a + h \right) - f\left( a \right)}{h}&=\frac{9 - 6 a + 6 a + 6 h - 9}{h}\\\frac{f\left( a + h \right) - f\left( a \right)}{h}&=\frac{6 h}{h}\\\frac{f\left( a + h \right) - f\left( a \right)}{h}&=6\\\end{aligned}$$