Exponential function

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Given the exponential function f(x)=a^x show that (a) f(u+v)=f(u) * f(v) and (b) f(2x)=[f(x)]^2

Nov 8th, 2014

f(u+v) = a^(u+v) = a^(u+v)=(a^u)*(a^v)=f(u)*f(v)

Remember that when you multiply exponential functions, you add the exponents if the bases of the functions are the same.  Therefore, a^(u+v) = (a^u)*(a^v) = f(u)*f(v)

f(2x) = a^(2x)=a^(x*2)=(a^x)^2=[f(x)]^2

When you raise an exponent to an exponent (a^x)^2, you can multiply those exponents (a^x)^2 = a^(2x).  This problems asks you to go in reverse and notice that a^(2x) is the same as a^(x*2), which is the same as [a^x]^2.

Nov 8th, 2014

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Nov 8th, 2014
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