Question

Find the value of $f\left(a\right),f\left(a+h\right),\frac{f\left(a+h\right)-f\left(a\right)}{h}$for the function $f\left(x\right)=5-2x$.

Short answer

The value of$f\left(a\right)=5-2a,f\left(a+h\right)=5-2a-2h,\frac{f\left(a+h\right)-f\left(a\right)}{h}=-2$

Step-by-step solution

Step 1. Evaluate the values of fa and fa+h.

From the given function,

$f\left(x\right)=5-2x\mathrm{....}\left(1\right)$

Evaluate $f\left(a\right)\text{and}f\left(a+h\right)$gives,

role="math" localid="1644532209360" $$\begin{gathered} f\left(a\right)=5-2\left(a\right)\mathrm{....}\left(\text{Substitute}x=a\text{in}\left(1\right)\right) \\ =5-2a \\ f\left(a+h\right)=5-2\left(a+h\right)\mathrm{....}\left(\text{Substitute}x=a+h\text{in}\left(1\right)\right) \\ =5-2a-2h \end{gathered}$$

Step 2. Subtract fa from fa+h and divide by h.

Evaluate $\frac{f\left(a+h\right)-f\left(a\right)}{h}$gives,

localid="1646153558178" $$\begin{gathered} \frac{f\left(a+h\right)-f\left(a\right)}{h}=\frac{\left(5-2a-2h\right)-\left(5-2a\right)}{h} \\ =\frac{5-2a-2h-5+2a}{h} \\ =-2 \end{gathered}$$

Step 3. Description of steps.

The value of $f\left(a\right)=5-2a,f\left(a+h\right)=5-2a-2h,\frac{f\left(a+h\right)-f\left(a\right)}{h}=-2$.