A logarithmic composite on a finite domain

A logarithmic composite on a finite domain

5 marks

TGM Original

Let f(x)=ln x, x>0, and g(x)=3-x2, -3 <= x 3. Find fg(x) on its largest restricted domain and state its range.

Solution:

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Answer:\(\ln(3-x^2)\); domain \((-\sqrt3,\sqrt3)\); range \((-\infty,\ln3]\).

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