Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

For an exponential function, $f\left(x\right)=C{a}^x,\frac{f(x+1)}{f\left(x\right)}=$

Step-by-Step Solution

Answer

The value of the function $\frac{f(x+1)}{f\left(x\right)}$ is $a$

Step 1. Given

The exponential function $f\left(x\right)=C{a}^x=\frac{f(x+1)}{f\left(x\right)}$

To find the value of given function

Step 2. Find the value of f ( x + 1 ) , f ( x )

$f\left(x\right)=C{a}^x$

Similarly, $$\begin{gathered} f(x+1)=C{a}^{x+1} \\ =C{a}^x.a \end{gathered}$$

Step 3. Solve the function

Solve the equation 

$$\begin{gathered} \frac{f(x+1)}{f\left(x\right)}=\frac{C{a}^x.a}{C{a}^x} \\ =a \end{gathered}$$