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Exponential functions 
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#1
Nov2912, 09:40 AM

P: 19

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
Nov2912, 12:06 PM

Sci Advisor
HW Helper
P: 11,894

A function is not defined in the absence of domain and range. So do tell us the whole definition as worded by your book.



#3
Nov2912, 01:01 PM

P: 905

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