What is the inverse of the function f(x) = (-12x - 7)/(x + 3)?

What is the inverse of the function f(x) = (-12x - 7)/(x + 3)?

• A. (-3x - 7)/(x + 12)
• B. (3x - 7)/(12x - 1)
• C. ((-3x - 7)/(x + 12))
• D. (12x + 7)/(-3x - 1)

Answer: (A)

To determine the inverse of the function f(x) = \((-12x - 7)/(x + 3)\), we start by letting y be equal to f(x): \[ y = \frac{-12x - 7}{x + 3} \] Next, to find the inverse, we switch the roles of y and x, and then solve for y: \[ x = \frac{-12y - 7}{y + 3} \] Multiplying both sides by (y + 3) to eliminate the fraction gives: \[ x(y + 3) = -12y - 7 \] Expanding the left side results in: \[ xy + 3x = -12y - 7 \] Reorganizing the equation to isolate terms containing y on one side yields: \[ xy + 12y = -7 - 3x \] Factoring y out from the left side results in: \[ y(x + 12) = -7 - 3x \] Finally, dividing both sides by the expression (x + 12) provides the expression for y: \[ y = \frac{-7 - 3x}{x + 12} \] This simplifies

To determine the inverse of the function f(x) = ((-12x - 7)/(x + 3)), we start by letting y be equal to f(x):

[ y = \frac{-12x - 7}{x + 3} ]

Next, to find the inverse, we switch the roles of y and x, and then solve for y:

[ x = \frac{-12y - 7}{y + 3} ]

Multiplying both sides by (y + 3) to eliminate the fraction gives:

[ x(y + 3) = -12y - 7 ]

Expanding the left side results in:

[ xy + 3x = -12y - 7 ]

Reorganizing the equation to isolate terms containing y on one side yields:

[ xy + 12y = -7 - 3x ]

Factoring y out from the left side results in:

[ y(x + 12) = -7 - 3x ]

Finally, dividing both sides by the expression (x + 12) provides the expression for y:

[ y = \frac{-7 - 3x}{x + 12} ]

This simplifies