Chapter 4.4, Problem 68AYU

To determine

To calculate:

The solution of following inequality equation as $f\left(x\right)\le g\left(x\right)$ draw both graphs of the function together:

  $\begin{array}{l}f\left(x\right)=x^4-1\\ g\left(x\right)=x-1\end{array}$

Answer to Problem 68AYU

The solution of following function with the inequality $f\left(x\right)\le g\left(x\right)$ is $x=0,\pm 1$ .

Explanation of Solution

Given information:

  $\begin{array}{l}f\left(x\right)=x^4-1\\ g\left(x\right)=x-1\\ f\left(x\right)\le g\left(x\right)\end{array}$

Calculation:

The two functions are given as:

  $\begin{array}{l}f\left(x\right)=x^4-1\\ g\left(x\right)=x-1\end{array}$

Use the inequality given in the problem:

  $\begin{array}{l}f\left(x\right)\le g\left(x\right)\\ x^4-1\le x-1\\ x^4-1-x+1\le 0\\ x\left(x^3-1\right)\le 0\\ x=0\\ OR\text{}\\ x^3-1=0\\ x^3=1\\ x=1\end{array}$

And the graph of two given function is below shown:

  

Conclusion:

Hence, solution of function is as $x=0,\pm 1$ .