
#1
Aug2213, 12:09 PM

P: 1

f(x) where x belongs to all real numbers
inverse: f1(x), where x belongs to all real numbers True or False: The inverse of f(x+3) is f1(x+3) My ideas: I think that it is false given that when you usually find the inverse of a function, you switch the x and y variables and solve for y again meaning that the inverse couldn't stay the same. I figured since the domain and range of f(x) belong to all real numbers, possibly f(x) = x and then inputting f(x+3) = x+ 3 then y = x+3 then y = x  3 but im not really sure if thats right :s 



#2
Aug2213, 01:49 PM

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#3
Aug2213, 04:14 PM

P: 35

Good Day michellemich!
If you are not sure of your answer, try some composition: let your original function be f(x)and your questionable inverse function be g(x) Evaluate (f of g) and (g of f). If they undo each other, they are inverses. 



#4
Aug2213, 06:26 PM

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Question regarding inverse functions
If you want to know if this is true for all invertible functions, it is simple enough to find a counterexample.
If, say, f(x)= 2x+ 3, then [itex]f(x)= 3x 2[/itex], then [itex]f^{1}(x)= (x+ 2)/3[/itex]. f(x+3)= 3(x+ 3) 2= 3x+ 7. The inverse of that function is [itex](x 7)/3[/itex]. Is that equal to [itex]f^{1}(x+ 3)= (x+3+ 2)/3= (x+ 5)/3[/itex]? 


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