Given the function f(x)=2^x and g(x)=log x, determine the range of the combined function y=f(x)g(x) Please explain how to find the range without using graphing technology.

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We have the two functions f(x)=2^x and g(x)=log x. The combined function y = f(x)*g(x).

y = 2^x * log x

Now the range of a function is the set of all values of y that can be obtained by using the function.

Here we see that log (x) takes on all real values. 2^x can take on all positive values.

So for the function y = 2^x * log x, the domain can be any value as multiplying a negative number by a positive number can yield a negative number.

Therefore the range is all real numbers from -inf. to + inf.

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