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Notice that the x is now in the exponent and the base is a fixed number. This is exactly the
opposite from what we’ve seen to this point. To this point the base has been the variable, x in
most cases, and the exponent was a fixed number. However, despite these differences these
functions evaluate in exactly the same way as those that we are used to. We will see some
examples of exponential functions shortly.
Before we get too far into this section we should address the restrictions on b. We avoid one and
zero because in this case the function would be, f ( x ) = 0x = 0 f ( x ) = 1x = 1 and and these are constant functions and won’t have many of the same properties that general
exponential functions have.
Next, we avoid negative numbers so that we don’t get any complex values out of the function
evaluation. For instance if we allowed b = -4 the function would be, f ( x ) = ( -4 ) x Þ 1
f ç ÷ = ( -4 ) 2 = -4
è2ø and as you can see there are some function evaluations that will give complex numbers. We only
want real numbers to arise from function evaluation and so to make sure of...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12