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inverse functions

# inverse functions - MAC1105 Inverse Functions When a task...

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2 b. Function f multiplies the input by 3. Define a function that divides by 3, namely x g(x) 3 = . Proceeding as before, we obtain a similar result. ( ) ( ) ( ) 3x (g f )(x) g f(x) g 3x x 3 x x (f g)(x) f g(x) f 3 x 3 3 = = = = = = ° ± ° ± ° ± ° ± = = = = ² ³ ² ³ ´ µ ´ µ ° ° c. This is a two-step function. Undoing each step in reverse order will generate the steps for g . f g 1. multiplies by 3 1. subtracts 5 2. adds 5 2. divides by 3 Using the above steps for g we can now write x 5 g(x) 3 - = . Let’s verify that these two functions undo one another. ( ) ( ) ( ) ( ) ( ) 3x 5 5 3x (g f )(x) g f(x) g 3x 5 x 3 3 x 5 x 5 (f g)(x) f g(x) f 3 5 x 5 5 x 3 3 + - - = = + = = = - - - - ° ± ° ± ° ± ° ± ± ± = = = + = - + = = ² ³ ² ³ ² ³ ² ³ ³ ³ ´ µ ´ µ µ ° ° Functions which undo one another are called inverses .
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