Final answer:
The inverse of the function y = 9x² -12x+ 4 can be found by swapping the x and y variables and solving for y. Domain restrictions for the inverse function are necessary to ensure that the resulting function is well-defined.
Step-by-step explanation:
The inverse of the function y = 9x² -12x+ 4 can be found by swapping the x and y variables and solving for y. Let's do that:
1. Start with the original function: y = 9x² -12x+ 4
2. Swap the x and y variables: x = 9y² -12y+ 4
3. Rearrange the equation to solve for y: 9y² -12y+ 4 -x = 0
4. Use the quadratic formula to solve for y:
y = (-b +/- sqrt(b²-4ac))/(2a)
For the given function, a = 9, b = -12, and c = 4-x. You can plug these values into the quadratic formula to calculate the inverse function.
Domain restrictions for the inverse function are necessary to ensure that the resulting function is well-defined. In this case, the domain restrictions would be determined by the range of the original function. Since the original function is a quadratic, the range may be restricted to certain values. It is important to check the range of the original function and set domain restrictions accordingly for the inverse function.