Gr12 Mathematics: Ch 2.3 Linear Functions
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Questions and Answers

What is the primary purpose of finding the inverse of a linear function?

  • To simplify the function
  • To find the domain and range of the function
  • To graph the function
  • To interchange the roles of the dependent and independent variables (correct)
  • What is the first step in finding the inverse of a linear function?

  • Express in function notation
  • Solve for y
  • Interchange x and y
  • Start with the function (correct)
  • What is the resulting form of the inverse of a linear function?

  • Exponential function
  • Quadratic function
  • Rational function
  • Linear function (correct)
  • What is the domain and range of the inverse function, assuming a ≠ 0?

    <p>Domain: ℝ, Range: ℝ</p> Signup and view all the answers

    What is the formula for the inverse of a linear function, given y = ax + q?

    <p>y = 1/a x - q/a</p> Signup and view all the answers

    What is the effect of interchanging the roles of the dependent and independent variables when finding the inverse of a linear function?

    <p>It swaps the domain and range of the function.</p> Signup and view all the answers

    What is the result of solving for y in the equation x = ay + q?

    <p>y = (1/a)x - (q/a)</p> Signup and view all the answers

    Why is the inverse of a linear function also a linear function?

    <p>Because the steps to find the inverse do not change the linearity of the function.</p> Signup and view all the answers

    What is the purpose of expressing the inverse function in function notation?

    <p>To clearly distinguish it from the original function.</p> Signup and view all the answers

    What can be said about the graph of the inverse of a linear function?

    <p>It is a line.</p> Signup and view all the answers

    If f(x) = 2x + 3, what is the value of f^{-1}(5)?

    <p>4</p> Signup and view all the answers

    Given a linear function f(x) = ax + q, which of the following statements is TRUE about the graph of its inverse function?

    <p>It is a reflection of the original function across the line y = x.</p> Signup and view all the answers

    What is the y-intercept of the inverse function of f(x) = 3x - 2?

    <p>-2/3</p> Signup and view all the answers

    If f(x) = -x + 1, what is the value of f^{-1}(-2)?

    <p>-3</p> Signup and view all the answers

    Given a linear function f(x) = ax + q, what can be said about the relationship between the slopes of f(x) and its inverse function?

    <p>They are multiplicative inverses.</p> Signup and view all the answers

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