The possible functions for f and g are f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
What is an exponential function?
An exponential function is a mathematical function of the following form: f ( x ) = [tex]p^{x}[/tex] where x is a variable, and p is a constant called the base of the function. The most commonly encountered exponential function base is the transcendental number e.
Analysis:
If for every value of x being positive and y is a positive whole number and for every x being negative y is a positive fraction, then that exponential function has a whole number base, Other wise it would have a fractional base. From the above explanation, f has (1,3) (positive x and whole number y) and (-1, 1/3) (negative x and positive fraction y). so therefore f has a whole number base and g has a fraction base.
Therefore f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
Learn more about exponential functions: brainly.com/question/2436547
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