A student was asked to find the inverse of the function f(x)=3x-7.
The student began the solution with the following:
Write f(x) = 3x-7 as y = 3x-7
x= 3y-7
The student eventually got the right answer for f^(-1)(x) [inverse notation] but did not get full marks for the solution. Why not?
he got x as a function of y, but did not illustrate that
f^-1(x) = (x+7)/3
The student did not receive full marks for the solution because their method of finding the inverse function was not entirely correct. Although they correctly started by rewriting the original function as y = 3x-7, they made an error when trying to solve for x in terms of y.
The correct process for finding the inverse function f^(-1)(x) involves interchanging the x and y variables and solving for y. Here's the proper way to do it:
1. Start with the equation: y = 3x-7
2. Interchange the x and y variables: x = 3y-7
3. Solve the equation for y:
x + 7 = 3y
(x + 7)/3 = y
4. Replace y with f^(-1)(x): f^(-1)(x) = (x + 7)/3
In this case, the student did not correctly solve for y in terms of x, which resulted in an incorrect inverse function. Therefore, the student did not receive full marks for the solution. It's important to follow the correct steps and apply the appropriate algebraic operations to ensure the accuracy of the solution.