Answer:
Explanation:
To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:
Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.
Swap the x and y variables: x = 3y + 7.
Solve for y:
Subtract 7 from both sides to get x - 7 = 3y.
Divide both sides by 3 to get (x - 7) / 3 = y.
Write the inverse function using f^-1(x) instead of y:
f^-1(x) = (x - 7) / 3
So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.