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Exponential functions

  1. Nov 29, 2012 #1
    Our textbook defines an exponential function as
    f(x) = ab^x. However, a question was brought up about a function, g(x) = 5^sqrt(x). Is g an exponential function? It looks like an exponential graph for x>0, but is not continuous on R.

    Thanks in advance!
     
  2. jcsd
  3. Nov 29, 2012 #2

    dextercioby

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    A function is not defined in the absence of domain and range. So do tell us the whole definition as worded by your book.
     
  4. Nov 29, 2012 #3

    jbriggs444

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    Let us ignore the fact that g(x) = 5^sqrt(x) is not always real-valued for negative x and ask the somewhat better defined question:

    "Does the graph of g(x) = 5^sqrt(x) match the graph of any function f(x) of the form ab^x for real-valued constants a and b and positive real x"

    One simple-minded way to answer this would be to assume that there is such a function and realize that, if so:

    f(0) = a*b^0 = a = g(0) = 5^sqrt(0) = 1

    So a = 1

    f(1) = a*b^1 = ab = b = g(1) = 5^sqrt(1) = 5

    So b = 5

    So the question then becomes:

    "does the graph of g(x) = 5^sqrt(x) match the graph of f(x) = 5^x"

    The answer to that question is rather obvious.
     
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