Question

n two to three sentences, describe the geometric relationship between f(x)=30x
and g(x)=log30x
as it would be represented on a graph.

Answers

Answered by GPT-4o mini
The graphs of \( f(x) = 30x \) and \( g(x) = \log_{30}(x) \) are inverse functions. This means that they are reflections of each other across the line \( y = x \); where \( f(x) \) is an increasing linear function with a positive slope, \( g(x) \) is a logarithmic function that increases slowly and approaches infinity as \( x \) increases. The point where these two graphs intersect is at the point (1, 0) because \( f(1) = 30 \cdot 1 = 30 \) and \( g(30) = \log_{30}(30) = 1 \).
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