|Nov29-12, 09:40 AM||#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!
|Nov29-12, 12:06 PM||#2|
Blog Entries: 9
A function is not defined in the absence of domain and range. So do tell us the whole definition as worded by your book.
|Nov29-12, 01:01 PM||#3|
"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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