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### High School Mathematics8.5 Inverse Relation or Inverse Functions

 Inverse Relation: If R is a relation from set A into another set B, then by interchanging the first and second coordinates or ordered pairs of R we get a new relation. This relation is called the inverse relation of R and is denoted by R-|. Set builder form, R-| = {(y,x)/(x,y) Î R}. Note: Domain and range of R-| are respectively range and domin of R. Inverse Functions: To find the inverse of a function written as an equation, interchange the two variables x and y and solve for y. If the inverse is also a function, it is denoted by f-1 Example 1: Find the inverse of the function {(3,4),(5,6),(7,8),(9,10)}. State the domain and range of this inverse. State if the inverse is also a function. Original function: {(3,4),(5,6),(7,8),(9,10)} Interchange the first and second coordinates in each pair. Inverse of the function: {(4,3),(6,5),(8,7),(10,9)} domain: {4,6,8,10} range: {3,5,7,9} Since each element in the domain of the inverse maps onto one and only one element in the range, the inverse of the original function is also a function. Example 2: Find the inverse of the function y = 2x + 4. Original function: y = 2x + 4 Domain of f: {x: x is real} Range of f: {y: y is real} To find the inverse of the function interchange x and y x = 2y + 4 x/2 - 4 = 2y x/2 - 2 = y Therefore the inverse function f-1 is: y = x/2 - 2 Domain of f-1: {x: x is real} Range of f-1: {y: y is real} Directions: Choose the correct answer. Also write at least ten examples of your own.

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### High School Mathematics8.5 Inverse Relation or Inverse Functions

 Q 1: Find the inverse of relation or function: y = 4x - 1x = 4y + 1x = 4/y - 1/yy = x/4 + 1/4 Q 2: Find the inverse of the function: {(1,3),(2,3),(4,5),(9,5)}{(3,1),(3,2),(5,4),(5,9)}{(1,3),(2,3),(4,5),(9,5)}Not a function Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!