Answer:
[tex]g'(x) = \frac{x^2}{100} +2[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 10\sqrt{x - 2[/tex]
Required
Determine the inverse function
[tex]g(x) = 10\sqrt{x - 2[/tex]
Replace g(x) with y
[tex]y = 10\sqrt{x -2[/tex]
Swap the positions of x and y
[tex]x = 10\sqrt{y -2[/tex]
Divide through by 10
[tex]\frac{x}{10} = \sqrt{y - 2[/tex]
Square of both sides
[tex]\frac{x^2}{100} = y - 2[/tex]
Make y the subject
[tex]y = \frac{x^2}{100} +2[/tex]
Replace y with g'(x)
[tex]g'(x) = \frac{x^2}{100} +2[/tex]
Hence, the inverse function is: [tex]g'(x) = \frac{x^2}{100} +2[/tex]
