Find the inverse funciton:
g(x) = 3x^4, x > 0
y=3x^4
inverse:
u switch the x and y:
x=3y^4
now u solve for y:
x/3=y^4
fourth root of x/3=y
To find the inverse function of g(x) = 3x^4, x > 0, we can follow these steps:
Step 1: Replace g(x) with y.
y = 3x^4
Step 2: Swap the roles of x and y.
x = 3y^4
Step 3: Solve the equation for y.
Divide both sides by 3:
x/3 = y^4
Step 4: Take the fourth root of both sides.
(x/3)^(1/4) = y
Step 5: This expression represents the inverse function of g(x).
The inverse function is: f(x) = (x/3)^(1/4)
Note that the domain and range of the inverse function will be the same as the original function, which is x > 0.