If \(f: R \rightarrow R\) is defined as \(f(x) = 3x + 2\), then what is \(f^{-1}(x)\)?

Given the binary operation \(*\) defined on the set of real numbers \(R\) by \(a * b = a + b - ab\), where \(a, b \in R\). What is the identity element of this operation?

If a function \(f: A \rightarrow B\) is bijective, which of the following statements is true?

Let \(R\) be a relation on the set \(A = \{1, 2, 3\}\) defined by \(R = \{(1,2), (2,3), (3,1)\}\). Which type of relation is \(R\)?

Consider the function \(f(x) = \frac{5x - 7}{2}\). Find the value of \(f^{-1}(4)\).

Let \(f: \mathbb{Z} \rightarrow \mathbb{Z}\) be defined by \(f(n) = 2n + 1\). Is the function \(f\) injective, surjective, both, or neither over the set of integers \(\mathbb{Z}\)?

If the set \(A = \{1, 2, 3, 4\}\) and the set \(B = \{a, b, c, d\}\) are in a relation \(R\) defined by \(R = \{(1, a), (2, b), (3, c), (4, d)\}\), which of the following properties does \(R\) satisfy?

If the function \(f: \mathbb{R} - \{3\} \rightarrow \mathbb{R}\) is defined as \(f(x) = \frac{2x + 1}{x - 3}\), then what is the range of \(f\)?

A binary operation \(\circ\) on the set of integers \(\mathbb{Z}\) is defined as \(a \circ b = a + b - 3\) for \(a, b \in \mathbb{Z}\). What is the identity element of \(\circ\)?

If \(g(x) = x^2 + 2x + 1\), what is the domain of the inverse function \(g^{-1}(x)\)?