Problem
Question 15 Find the inverse of the one-to-one function. \[ f(x)=-3 x-6 \] \[ f^{-1}(x)= \] (A) \[ \frac{x-6}{-3} \] \[ f^{-1}(x)= \] B \[ f^{1}(x)= \] (C) \[ \frac{y+6}{-3} \] \[ f^{-1}(x)= \] D \[ \frac{x+6}{-3} \]
Solution
Step 1 ：Let $y = -3x - 6$. Then $y = -3x - 6$
Step 2 ：Solve for x: $x = \frac{y + 6}{-3}$
Step 3 ：Hence, the inverse function is given by $f^{-1}(x) = \boxed{\frac{x + 6}{-3}}$
