When I write the inverse function for y = 3x - 7, can I change y to f^-1(x)?
Yes, you can change the variable "y" to "f^-1(x)" when writing the inverse function of "y = 3x - 7". The notation "f^-1(x)" represents the inverse function of "f(x)".
To find the inverse function, you can follow these steps:
1. Start with the equation of the original function: y = 3x - 7.
2. Replace "y" with "f^-1(x)": f^-1(x) = 3x - 7.
3. Swap the positions of "x" and "f^-1(x)": x = 3f^-1(x) - 7.
4. Solve the equation for "f^-1(x)".
a. Add 7 to both sides: x + 7 = 3f^-1(x).
b. Divide both sides by 3: (x + 7) / 3 = f^-1(x).
c. Simplify: f^-1(x) = (x + 7) / 3.
Therefore, the inverse function of y = 3x - 7 is f^-1(x) = (x + 7) / 3.