# 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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### 2 Answers

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.**

f(x)= 2^x and g(x) = logx.

Therefore fog(x) = 2^g(x)

=> fog(x) = 2^logx.

y = 2^logx

logx is not defined for negative values of x.

y = 2^logx is defined only for x > 0 for which y > 0.

At x = 0, y is not defined.

Therefore y > 0. Or y is in the set {0 infinity} - {0}.

Therefore the range of the function y = fog(x) = 2^logx is {0, infinity}- (0}.