+0

0
117
1

What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

Jul 11, 2018

#1
+20850
+1

What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

$$\begin{array}{|rcll|} \hline (x-3)^2+(x-8)^2 &=& 0 \\ x^2-6x+9-x^2+16x-64 &=& 0 \\ 10x +9 - 64 &=& 0 \\ 10x - 55 &=& 0 \\ 10x &=& 55 \\ \mathbf{x}& \mathbf{=} & \mathbf{5.5} \\ \hline \end{array}$$

The smallest real number x in the domain of the function is 5.5

Jul 11, 2018

#1
+20850
+1

What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

$$\begin{array}{|rcll|} \hline (x-3)^2+(x-8)^2 &=& 0 \\ x^2-6x+9-x^2+16x-64 &=& 0 \\ 10x +9 - 64 &=& 0 \\ 10x - 55 &=& 0 \\ 10x &=& 55 \\ \mathbf{x}& \mathbf{=} & \mathbf{5.5} \\ \hline \end{array}$$

The smallest real number x in the domain of the function is 5.5

heureka Jul 11, 2018