If f(x) = 3x - 7, what is f^{-1}(x)?

If f(x) = 3x - 7, what is f^{-1}(x)?

• A. 3x - 7
• B. x/3 - 7
• C. (x + 7)/3
• D. (x - 7)/3

Answer: (C)

Finding an inverse means swapping the roles of inputs and outputs. Start by letting y = f(x) = 3x - 7. Solve for x in terms of y: y + 7 = 3x, so x = (y + 7)/3. Since the inverse swaps x and y, you replace y with x to get f^{-1}(x) = (x + 7)/3. This matches the general rule for inverting a linear function ax + b: the inverse is (x − b)/a, and with a = 3 and b = -7, you get (x + 7)/3. To check, f(f^{-1}(x)) = 3*(x + 7)/3 - 7 = x, and f^{-1}(f(x)) = ((3x - 7) + 7)/3 = x.

Finding an inverse means swapping the roles of inputs and outputs. Start by letting y = f(x) = 3x - 7. Solve for x in terms of y: y + 7 = 3x, so x = (y + 7)/3. Since the inverse swaps x and y, you replace y with x to get f^{-1}(x) = (x + 7)/3. This matches the general rule for inverting a linear function ax + b: the inverse is (x − b)/a, and with a = 3 and b = -7, you get (x + 7)/3. To check, f(f^{-1}(x)) = 3*(x + 7)/3 - 7 = x, and f^{-1}(f(x)) = ((3x - 7) + 7)/3 = x.