Finding Inverse Functions (2.7.1)

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Presentation transcript:

Finding Inverse Functions (2.7.1) October 31st, 2016

Definitions *function: A relation such that for every value of x, there is only one value of y (must pass the vertical line test) *one-to-one: A relation in which each point in a set is mapped onto exactly one other point (must pass the horizontal line test) *inverse operation: the operation that reverses the effect of another operation *inverse function: The function that results from switching the x- and y-variables in a given function; the inverse of a function called f(x) is called f -1(x); the graph of an inverse is a reflection of the original function over the line y=x

Finding Inverse Functions Step 1: Replace f(x) with y. Step 2: Switch x and y. Step 3: Solve for y. Step 4: Replace y with f -1(x).

Ex. 1: You are driving home at a steady speed, and your distance from home, in miles, can be represented by f(x) = -20x+15, where x is your driving time in hours. (a) What are the independent and dependent variables? Explain what they mean in the context of the problem. Draw a graph of f(x) and given the reasonable domain and range of the function. (b) Find the inverse function f -1(x). What are the independent and dependent variables? Explain what they mean in the context of the problem. Draw a graph of and give the reasonable domain and range of the function. f -1(x)

***The inverse function only exists when the original function is one-to-one. Sometimes, we restrict the domain of the original so that we can write an inverse function.

Ex. 2: Find the inverse of each function Ex. 2: Find the inverse of each function. State the domain and range of both the function and its inverse. Restrict the domain of the function if needed.