If f(x) and g(x) are inverses, which of the following must be true? I. f(x) is a reflection of g(x) over the line y = x. II. f(x) is a reflection of g(x) over the y-axis. III. f(g(x)) = x I only II only I and II only I and III only
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This is because the inverse function undoes the original function, resulting in a reflection over the line Y = X. Show more…
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Let $f(x)=x^{2}, x>1,$ and $g(x)=\sqrt{x}$ (a) Show that $f(g(x))=x, x>1,$ and $g(f(x))=x$ $x>1$ (b) Show that $f$ and $g$ are not inverses by showing that the graphs of $y=f(x)$ and $y=g(x)$ are not reflections of one another about $y=x$ (c) Do parts (a) and (b) contradict one another? $\mathrm{Ex}-$ plain.
BEFORE CALCULUS
Inverse Functions; Inverse Trigonometric Functions
Determine whether each pair of functions $f$ and $g$ are inverses of each other. $$f(x)=2 x \text { and } g(x)=0.5 x$$
Additional Function Topics
Inverse Functions
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