1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Exponential functions
  1. Exponential Functions (Replies: 6)

  2. Exponential function (Replies: 4)

  3. Exponential function (Replies: 3)

  4. Exponential function (Replies: 7)

Loading...