Inverse functions

• f^-1(x) - the inverse function of f(x)

  • f^-1(f(x)) = f(f^-1(x)) = x

  • domain of f(x) = range of f^-1(x)

  • range of f(x) = domain of f^-1(x)

• to check if a plot graphed on a plane is an inverse function, do the horizontal line test: draw a horizontal line on each plot. if it only intersects 1 point, then its a inverse function. if it intersects multiple, then it is not

• to find inverse, switch x and y, then solve for y

  • ex; f(x) = -2x - 1

    • y = -2x - 1

    • x = -2y - 1

    • y = -1/2x - 1/2

SOLVE f^-1(x) = 5x + 2 / x - 3

• y = 5x + 2 / x - 3

• x = 5y + 2 / y - 3

• x (y-3) = 5y + 2

  • to inverse division, multiply

• xy - 3x = 5y + 2

• - 3x = 5y - xy + 2

• -3x - 2 = 5y - xy

• -3x - 2 = y(5-x)

• -3x - 2 / 5 - x

  • to inverse multiplication, divide