A = {a, b, c, d} X = {1, 2, 3, 4} Select the definition for f that is a well-defined function. f = {(a, 2), (b, 3), (c, 3), (1, d)} f = {(a, 2), (b, 3), (b, 3), (d, 1)} f = {(a, 2), (b, 3), (d, 1)} f = {(a, 2), (b, 3), (c, 3), (d, 1)}
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A function $\mathrm{f}$ is constant from set $\mathrm{A}=\{1,2,3\}$ onto set $\mathrm{B}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ such that $\mathrm{f}(1)=\mathrm{a}$, then the range of $\mathrm{f}$ is (1) $\{\mathrm{a}, \mathrm{c}\}$ (2) $\{\mathrm{a}\}$ (3) $\{\mathrm{a}, \mathrm{b}\}$ (4) $\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$
Let $f_{1}(x)=x, f_{2}(x)=\frac{1}{x}, f_{3}(x)=1-x$, $f_{4}(x)=\frac{x}{x-1}, f_{5}(x)=\frac{1}{1-x},$ and $f_{6}(x)=\frac{x-1}{x}$. a) Determine the following. i) $f_{2}\left(f_{3}(x)\right)$ ii) $\left(f_{3} \circ f_{5}\right)(x)$ iii) $f_{1}\left(f_{2}(x)\right)$ iv) $f_{2}\left(f_{1}(x)\right)$ b) $f_{6}^{-1}(x)$ is the same as which function listed in part a)?
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