Chapter 6.3, Problem 4E

To determine

To choose: The odd one equation from all the equations and explain with reasoning.

Answer to Problem 4E

An odd one equation is $f\left(x\right)={\left(-3\right)}^x$ .

Explanation of Solution

Given information:

The four equations $y=3^x,f\left(x\right)=2\left(4^x\right),f\left(x\right)={\left(-3\right)}^x\text{ and }y=5{\left(3\right)}^x$ here, $x\text{ and }y$ are variables.

The exponential function the continuous function that is defined as $f\left(x\right)=a{b}^x$ where $b$ is the base such that $a\ne 0,b>0,b\ne 1$ and $x$ is the independent variable.

It can be seen that all the given equations are of the form $f\left(x\right)=a{b}^x$ except one function $f\left(x\right)={\left(-3\right)}^x$ .

The equation $f\left(x\right)={\left(-3\right)}^x$ has a negative base and rest of the equations have positive base.

The equation $f\left(x\right)={\left(-3\right)}^x$ does not satisfy the condition of exponential function since the value of $b$ is negative.

Therefore, the equation $f\left(x\right)={\left(-3\right)}^x$ is an odd equation in among all provided options.