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Core 3 Functions 3

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Starter The functions f and g are defined by Find an expression for gf in terms of x and state its domain and range. Sketch the graph of y = gf(x) showing the coordinates of any points of intersections with the coordinate axes. Show that, if the equation gf(x) – 2f(x) = a has no real roots, then a < –10.
 
Objective: to form inverse functions
Inverse Functions A function f cannot have an inverse function f -1 unless f is one-to-one (there must be a unique value y in the range of f for each value of x in the domain of f). The range of f is the domain of f -1 and vice versa.
Inverse Functions The graphs of a pair of inverse functions are reflections of each other in the line y = x.
Examples Find the inverse of the functions f and g.
 
 
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Core 3 Functions 3

  • 1. Starter The functions f and g are defined by Find an expression for gf in terms of x and state its domain and range. Sketch the graph of y = gf(x) showing the coordinates of any points of intersections with the coordinate axes. Show that, if the equation gf(x) – 2f(x) = a has no real roots, then a < –10.
  • 2.  
  • 3. Objective: to form inverse functions
  • 4. Inverse Functions A function f cannot have an inverse function f -1 unless f is one-to-one (there must be a unique value y in the range of f for each value of x in the domain of f). The range of f is the domain of f -1 and vice versa.
  • 5. Inverse Functions The graphs of a pair of inverse functions are reflections of each other in the line y = x.
  • 6. Examples Find the inverse of the functions f and g.
  • 7.  
  • 8.  
  • 9. Core 3 & 4 Textbook Exercise 2C Page 35 Questions 12 to 18