Pure Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — The inverse function

About this lesson

This unit introduces the concept of the inverse function. It begins with a real-life example involving a father-daughter relation to illustrate the idea of a relation and its inverse, and whether each is a function. The unit then defines the inverse function for one-to-one functions, explains how to find it algebraically by exchanging variables and solving for y, and shows that the graph of a function and its inverse are symmetric about the line y = x. It also covers the domain and range of inverse functions, the horizontal line test for one-to-one functions, and the property that the composition of a function and its inverse yields the identity. Worked examples include linear functions, square root functions, and restricted domains to ensure invertibility. Exercises ask students to find inverses, determine domains, and identify errors in solutions.

Main topics in this lesson

  • Definition of inverse function
  • Finding inverse functions algebraically
  • Graphical representation and symmetry about y = x
  • Domain and range of inverse functions
  • Horizontal line test for one-to-one functions
  • Composition of function and inverse

Key terms and vocabulary

  • Inverse function
  • One-to-one function
  • Domain
  • Range
  • Horizontal line test
  • Vertical line test
  • Reflection in the line y = x

Questions and answers on Exponents, Logarithms and their Applications — The inverse function - practice and revision

Multiple choice questions on this lesson in Pure Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

إذا كانت f(x) = x² - 3 حيث x ≥ 0، فإن f⁻¹(1) تساوي:

  • 1 2
  • 2 4
  • 3 -2
  • 4 1
2

إذا كانت f(x) = 6 - 2x، فإن f⁻¹(x) تساوي:

  • 1 (6 - x)/2
  • 2 (x - 6)/2
  • 3 6 + 2x
  • 4 2x - 6
3

إذا كانت f(x) = x + 9، فإن تمثيل f و f⁻¹ بيانياً يكونان متماثلين حول:

  • 1 المستقيم y = x
  • 2 المستقيم y = -x
  • 3 محور السينات
  • 4 محور الصادات
4

إذا كانت f(x) = 2x + 5، فإن f⁻¹(f(3)) تساوي:

  • 1 3
  • 2 11
  • 3 5
  • 4 8
5

إذا كانت f(x) = √(x + 4)، فإن مجال الدالة العكسية f⁻¹ هو:

  • 1 [0, ∞)
  • 2 [-4, ∞)
  • 3 (-∞, 0]
  • 4 (-∞, ∞)
6

إذا كانت f(x) = 7x، فإن f⁻¹(14) تساوي:

  • 1 2
  • 2 98
  • 3 7
  • 4 1/2

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