Question

In 23 and 24 find $g \circ f$, $(g \circ f)^{-1}$, $g^{-1}$, $f^{-1}$, and $f^{-1} \circ g^{-1}$, and state how $(g \circ f)^{-1}$ and $f^{-1} \circ g^{-1}$ are related. 23. Let $X = \{a, c, b\}$, $Y = \{x, y, z\}$, and $Z = \{u, v, w\}$. Define $f: X \to Y$ and $g: Y \to Z$ by the arrow diagrams below. 24. Define $f: \mathbb{R} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ by the formulas $f(x) = x + 3$ and $g(x) = -x$ for all $x \in \mathbb{R}$.

          In 23 and 24 find $g \circ f$, $(g \circ f)^{-1}$, $g^{-1}$, $f^{-1}$, and $f^{-1} \circ g^{-1}$, and state how $(g \circ f)^{-1}$ and $f^{-1} \circ g^{-1}$ are related.
23. Let $X = \{a, c, b\}$, $Y = \{x, y, z\}$, and $Z = \{u, v, w\}$. Define $f: X \to Y$ and $g: Y \to Z$ by the arrow diagrams below.
24. Define $f: \mathbb{R} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ by the formulas $f(x) = x + 3$ and $g(x) = -x$ for all $x \in \mathbb{R}$.

$In 23 and 24 find g ∘ f, (g ∘ f)^-1, g^-1, f^-1, and f^-1∘ g^-1, and state how (g ∘ f)^-1 and f^-1∘ g^-1 are related. 23. Let X = {a, c, b}, Y = {x, y, z}, and Z = {u, v, w}. Define f: X → Y and g: Y → Z by the arrow diagrams below. 24. Define f: ℝ→ℝ and g: ℝ→ℝ by the formulas f(x) = x + 3 and g(x) = -x for all x ∈ℝ.$

Added by Victoria G.

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