Question

Let $ A=\left\{x \in \mathbb{R} \left\lvert\, x \neq-\frac{1}{2}\right.\right\} $ and function $ f: \mathrm{A} \rightarrow \mathbb{R} $ given by $ f(x)=\frac{3 x}{2 x+1} $. Show that it is one-to-one and find the range of it and $ f^{-1}(x) $. Task 5 (6 points) Let $ X=\{a, b\} $ and $ Y=\{1,2,3,4\} $. (a) How many one-to-one functions are there from $ X \rightarrow $ $ Y $ and $ Y \rightarrow X $ ? In each case, list all the functions. (b) How many onto functions are there $ X \rightarrow Y $ and $ Y \rightarrow X $ ? In each case, list all the functions.

          Let \( A=\left\{x \in \mathbb{R} \left\lvert\, x \neq-\frac{1}{2}\right.\right\} \) and function \( f: \mathrm{A} \rightarrow \mathbb{R} \) given by \( f(x)=\frac{3 x}{2 x+1} \). Show that it is one-to-one and find the range of it and \( f^{-1}(x) \).

Task 5 (6 points)
Let \( X=\{a, b\} \) and \( Y=\{1,2,3,4\} \).
(a) How many one-to-one functions are there from \( X \rightarrow \) \( Y \) and \( Y \rightarrow X \) ? In each case, list all the functions.
(b) How many onto functions are there \( X \rightarrow Y \) and \( Y \rightarrow X \) ? In each case, list all the functions.

$Let A={x ∈ℝ| x ≠-(1)/(2).} and function f: A→ℝ given by f(x)=(3 x)/(2 x+1). Show that it is one-to-one and find the range of it and f^-1(x). Task 5 (6 points) Let X={a, b} and Y={1,2,3,4}. (a) How many one-to-one functions are there from X → Y and Y → X ? In each case, list all the functions. (b) How many onto functions are there X → Y and Y → X ? In each case, list all the functions.$

Added by Dilnaz G.

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