Thursday, September 15, 2016
1.5 Inverse Relations
Discuss what you remember about inverse relations with the people around you. Try to answer the following questions:
• What type of notation indicates that something is an inverse function?
• Is the inverse of a function always a function?
• How do you create the graph of an inverse relation?
• How do you find the equation of an inverse relation?
• How are the domain and range of a function and its inverse related?
• How can you ensure that the inverse of a function is also a function?
One person in the pair should record your answers. They do not have to be right, but you are expected to try. You have ten minutes.
What type of notation indicates that something is an inverse function?
How do you find the equation of an inverse relation?
ex/ Write the inverse of f(x) = x3 + 3.
How do you create the graph of an inverse relation:
­ given a graph of the original function?
­ given a table of values for the original function?
­ given an equation for the original function?
How are the domain and range of a function and its inverse related?
Is the inverse of a function always a function?
How can you ensure that the inverse of a function is also a function?
ex/ A function g is defined by g(x) = 2(x ­ 1)2 + 3. a) Determine an equation for the inverse of g(x)
b) Sketch the graphs of g(x) and its inverse.
c) State the restrictions that need
to be applied to the domain or
range of g(x) so that its inverse is
also a function.