Final answer:
To find the inverse of each given function, switch the roles of x and y and solve for y. The inverse of options A, B, and C are 1-1(x) = (x + 3)/7, -1(x) = (3 - x)/7, and g(x) = (3 - x)/2, respectively. The inverse of option D is undefined.
Step-by-step explanation:
The inverse of a function is a function that undoes the action of the original function. To find the inverse of a function, we need to switch the roles of x and y and solve for y. Let's solve for the inverse of each given function:
A) First, change the equation to y = 7x - 3. Switching x and y, we get x = 7y - 3. Now solve for y: 7y = x + 3, y = (x + 3)/7. So, the inverse is 1-1(x) = (x + 3)/7.
B) In this case, switching x and y gives x = 3 - 7y. Solve for y: 7y = 3 - x, y = (3 - x)/7. Therefore, the inverse is -1(x) = (3 - x)/7.
C) The given function is already in the form g(x) = 3 - 2x/2. Switching x and y, we have x = 3 - 2y/2. Solve for y: 2y/2 = 3 - x, y = (3 - x)/2. Therefore, the inverse is g(x) = (3 - x)/2.
D) The function 1(x) = ? + 7 + 1 cannot be solved for the inverse with the given information, as there is a missing value to substitute for '?'. Therefore, the inverse of option D is undefined.