Homework SourseIf fx x3 2x and g is the inverse of f then g 3 is please
If f(x) = x3 + 2x and g is the inverse of f, then g\' (3) is ?
-please answer thoroughly
Solution
Let y=f(x)= x^3+2x
g(x) is f\'(x)
g\'(x) is /dx[f¹(x)]
dy/dx = 3x^2 + 2
dx/dy = 1/ (3x^2+2)
g\'(y) = 1/ (3x^2+2) ......
sothat if calculating the derivative (gradient ) of g if we know the output value of the function g by using this formula
The point we are interested in is (1,3) on the f(x).
ex,
y=f(x) , 3=f(1)
x=g(y) , 1=g(3)
g\'(3) = 1/ (3*1^2+2)
g\'(3) = 1/5
![If f(x) = x3 + 2x and g is the inverse of f, then g\' (3) is ? -please answer thoroughlySolutionLet y=f(x)= x^3+2x g(x) is f\'(x) g\'(x) is /dx[f¹(x)] dy/dx = 3](/WebImages/12/if-fx-x3-2x-and-g-is-the-inverse-of-f-then-g-3-is-please-1013426-1761523367-0.webp "If f(x) = x3 + 2x and g is the inverse of f, then g\' (3) is ? -please answer thoroughlySolutionLet y=f(x)= x^3+2x g(x) is f\'(x) g\'(x) is /dx[f¹(x)] dy/dx = 3")
