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Find the inverse of \newlinef(x)=−4x−12f(x)=-4x-12

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Absolute value and opposite integersright chevron icon

Full solution

Q. Find the inverse of \newlinef(x)=−4x−12f(x)=-4x-12
  1. Replace with y: To find the inverse of the function f(x)=−4x−12f(x) = -4x - 12, we need to swap the xx and yy, and then solve for yy. Let's start by replacing f(x)f(x) with yy:y=−4x−12y = -4x - 12
  2. Swap x and y: Now swap x and y to get the inverse relationship:\newlinex=−4y−12x = -4y - 12
  3. Add 1212 to both sides: Next, we need to solve for yy. Start by adding 1212 to both sides of the equation: x+12=−4yx + 12 = -4y
  4. Divide by −4-4: Now, divide both sides by −4-4 to isolate yy:y=x+12−4y = \frac{x + 12}{-4}
  5. Simplify the equation: Simplify the equation by distributing the division across the numerator: y=−14x−3y = -\frac{1}{4}x - 3 This is the inverse function of f(x)f(x).

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