Multiple Choice Question (MCQ)

If f(x) = 3x-1, n represents the slope of the line with the equation y = f^{-1}(x), and p represents the slope of a line that is perpendicular to the line with the equation y=f(x), then np=

  1. ×

    -9

  2. -\dfrac{1}{9}

  3. ×

    \dfrac{1}{9}

  4. ×

    9

  5. ×

    It cannot be determined from the information given.

Collected in the board: Coordinate geometry

Steven Zheng posted 2 months ago


Answer

  1. From the condition, the slope of f(x)=3x-1 is 3.

    Since the slopes of inverse functions are reciprocals, the slope of f(x)=3x-1 is \dfrac{1}{3} , that is

    n=\dfrac{1}{3}

    Since the slope of a line that is perpendicular to f(x) is a negative reciprocal of the slope of f(x), or -\dfrac{1}{3}, that is

    p = -\dfrac{1}{3}


    The product of n and p is -\dfrac{1}{9}

Steven Zheng posted 2 months ago

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