Consider the functions $f(x) = e^x - 1$ and $g(x) = \ln(x+k)$, where $k$ is a real number. Analyse the conditions on $k$ such that the composite function $f(g(x))$ exists. Determine an expression for $f(g(x))$ when it exists. Furthermore, find the largest possible domain of $f(g(x))$ in terms of $k$, and evaluate $f(g(1))$ assuming $k$ satisfies the conditions for the composite function to exist.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 6 marks, testing your understanding of Composition of Functions. It falls under Algebra, number and structure in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
composition of functions, where $f$ composite $g, f \circ g$, is defined by $(f \circ g)(x)=f(g(x))$ given $r_{g} \subseteq d_{f}$
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