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MathematicsGrade 12en

📐 Functions and Inverse Functions

This quiz explores the definition, properties, and applications of functions and their inverses at the Grade 12 level. **What you'll learn:** - Determine whether a relation is a function using the vertical line test - Find and verify inverse functions algebraically - Apply domain and range restrictions to ensure inverse functions exist - Compose functions and interpret their real-world meaning - Solve problems involving function transformations and inverses

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Questions in this quiz

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  1. Question 1

    Which of the following relations is a function?

  2. Question 2

    The function f(x)=x2f(x) = x^2 defined on all real numbers has an inverse function.

  3. Question 3

    If f(x)=2x+5f(x) = 2x + 5, then f−1(x)=f^{-1}(x) = ___

  4. Question 4

    If ff and gg are functions such that f(g(x))=xf(g(x)) = x for all xx in the domain of gg, then ff and gg are inverses of each other.

  5. Question 5

    Which statement about the graphs of a function ff and its inverse f−1f^{-1} is true?

  6. Question 6

    If f(x)=3x−2x+1f(x) = \frac{3x - 2}{x + 1}, then f−1(2)=f^{-1}(2) = ___

  7. Question 7

    If f(x)=x3−1f(x) = x^3 - 1 and g(x)=2x+3g(x) = 2x + 3, what is (f∘g)(2)(f \circ g)(2)?

  8. Question 8

    For a function to have an inverse, it must be both injective (one-to-one) and surjective (onto) its codomain.

  9. Question 9

    The function f(x)=x−4f(x) = \sqrt{x - 4} is defined on the domain [4,∞)[4, \infty). What is the range of f−1f^{-1}?

  10. Question 10

    Let f(x)=1x−3f(x) = \frac{1}{x - 3} with domain R∖{3}\mathbb{R} \setminus \{3\}. For f−1f^{-1} to be properly defined, what must be true about the range of ff?