Chapter 0.2, Problem 9QR

(a)

To determine

To find: The all real solutions to the given equation.

Answer to Problem 9QR

The solutions are equal to $3$ and $-3$ .

Explanation of Solution

Given information:

The function is $f\left(x\right)=x^2-5$ .

Calculation:

To calculate all real solution for $f\left(x\right)=4$ .

Substitute $f\left(x\right)=4$ in the given function $f\left(x\right)=x^2-5$ and solve for $x$ :

  $\begin{array}{c}4=x^2-5\\ x^2=4+5\\ x^2=9\\ x=\pm \sqrt{9}\\ x=\pm 3\end{array}$

Hence, the solutions are $3$ and $-3$ .

(b)

To determine

To find: The all real solutions to the given equation.

Answer to Problem 9QR

No real solutions.

Explanation of Solution

Given information:

The function is $f\left(x\right)=x^2-5$ .

Calculation:

To calculate all real solution for $f\left(x\right)=-6$ .

Substitute $f\left(x\right)=-6$ in the given function $f\left(x\right)=x^2-5$ and solve for $x$ :

  $\begin{array}{c}-6=x^2-5\\ x^2=-6+5\\ x^2=-1\\ x=\pm \sqrt{-1}\\ x=\pm i\end{array}$

So, there are no real solutions.

Hence, there are no real solutions.