6. Let e > 1 be the base of natural logarithm. We know that f(x) continuous and strictly monotone increasing on R. Let g(x) = f(x) = ln(x) be the inverse function of f. We know that ln(a') = b ln a...

Extracted text: 6. Let e > 1 be the base of natural logarithm. We know that f(x) continuous and strictly monotone increasing on R. Let g(x) = f(x) = ln(x) be the inverse function of f. We know that ln(a') = b ln a for any a > 0 and et : R → R is any be R. What's the range of f : R → R? Or equivalent, what's the domain of g(x)? You need to justify your steps. (b) Explain that g is continuous and strictly monotone increasing on its domain.