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Question 637552: Determine with reasons, whether the following functions are one to one.
(a) f(x)=x^3 + 3^x
(b) g(x)= 5ln(x^2+1)
Thanks heaps!
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! I'm not a wizard on this topic, but I think one to one means that for each value of x there is a unique value of f(x) or g(x). If so these are true functions, because for every real value of x you get a single value for f(x) or g(x). The ln bothered me, but the argument x^2 + 1 is always positive, thus ln(positive number) exists and unique (single valued). An example of a non one to one is f(x) = sqrt(x). If x=4, f(4) = + or - 2, two different values satisfy the f(x), thus not unique. These functions, especially g(x), may not hold for complex values of x.
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