Chapter 5, Problem 1CRQ

The function f(x) = x^b (b, a real number) is called a/an _____ function, whereas the function g(x) = b^x, where b > _____ and b ≠ _____, is called a/an function.

To determine

To fill: The statement “The function $f\left(x\right)=x^b$ is called as a        function, whereas the function $g\left(x\right)=b^x$, where       and        is called as an            function.”

Answer to Problem 1CRQ

The function $f\left(x\right)=x^b$ is called as a power function, whereas the function $g\left(x\right)=b^x$, where $b>0$ and $b\ne 1$ is called as an exponential function.

Explanation of Solution

The power function is defined as when a real number b is power of a variable x.

The exponential function is defined as when a variable x is power of a number b which is greater than zero and does not equal to zero.

Thus, the function $f\left(x\right)=x^b$ is called as a power function, whereas the function $g\left(x\right)=b^x$, where $b>0$ and $b\ne 1$ is called as an exponential function.