Let f(x) = \ln(7x-2) and g(x)=e^{7x-2} a. Find domain of f(x) b. Find domain of g(x) c. Find...

Question:

Let {eq}f(x) = \ln(7x-2) {/eq} and {eq}g(x)=e^{7x-2} {/eq}

a. Find domain of {eq}f(x) {/eq}

b. Find domain of {eq}g(x) {/eq}

c. Find {eq}f(1)+g(0) {/eq}

Domain of Exponential and Logarithmic Functions

Since exponential and logarithmic functions are inverses of one another, their domains are related. Specifically, the domain of a standard exponential function is all real numbers, but the range is all positive numbers. A logarithmic function has these two reversed, so the domain is all positive numbers and the range is all real numbers.

Answer and Explanation:

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a) We can only take a logarithm of a positive number. Thus, the domain of this function is whatever values of x allow the expression within the...

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