Inverse Linear Functions

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Presentation transcript:

Inverse Linear Functions 4-7

An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair in a relation. If (5,3) is an ordered pair of a relation, then (3,5) is an ordered pair of the inverse relation

Example A and B are inverse relations (-3,-16) (-1, 4) (2,4) (5,32) B

a. {(4,-10), (7, -19), (-5,17), (-3,11)} x -4 -1 5 9 y -13 -8.5 0.5 6.5 b.

Steps in finding the inverse function Replace f(x) with y in the equation for f(x) Interchange y and x in the equation Solve the equation for y Replace y with f-1(x) in the new equation

Find the inverse of f(x)=3x – 2

Find the inverse of each function f(x) = 4x – 8 c) f(x) = - ½ x + 11 f(x) = 4x – 12 d) f(x) = 1/3x + 7

Graph the inverse of each function

Randall wants to make a report on climate analysis Randall wants to make a report on climate analysis. He found a table of temperatures recorded in degrees celsius. He knows that a formula for converting degrees fahrenheit to degrees celsius is c(x) = 5/9(x-32). He will need to find the inverse function to convert from degrees Celsius to degrees fahrenheit.

Write the inverse of each notation in f-1(x) 3y – 12x = -72 3. -42 + 6y = x -7y + 2x = -28 4. 3x + 24 = 2x