Chapter 6, Problem 9ASAP

To determine

To find: the option that gives the value of expression less than 1.

Answer to Problem 9ASAP

D.

Explanation of Solution

Given information:

  $x>1$

The options are as follows:

1. $x^{x-1}$
2. $x^{x+2}$
3. ${\left(x+2\right)}^x$
4. $x^{1-x}$
5. $x^x$

Calculation:

Let the value of $x=2$ . Substitute the value on each equation and check the expression for value less than 1.

  $\begin{array}{c}{x}^{x-1}=2^{2-1}\\ =2\\ \\ x^{x+2}=2^{2+2}\\ =2^4\\ \\ {\left(x+2\right)}^x={\left(2+2\right)}^2\\ =4^2\\ \\ x^{1-x}=2^{1-2}\\ =2^{-1}\\ =0.5\\ \\ x^x=2^2\end{array}$

Since the value of $x^{1-x}$ is less than 1 for $x>1$ . Thus, option D is correct.