Question

Find domain and range of (answers should be subsets of R):

f(x)= 3/2x -1

Answer 1

Answer on Question #76191 – Math – Discrete Mathematics

Question

Find domain and range of (answers should be subsets of $\mathbb{R}$):

$$f(x) = \frac{3}{2x - 1}$$

Solution

$$f(x) = \frac{3}{2x - 1}$$ $$2x - 1 \neq 0 \Rightarrow x \neq \frac{1}{2}.$$

Domain: $\left\{x \in \mathbb{R} \mid x \neq \frac{1}{2}\right\}$.

$$\frac{3}{2x - 1} \neq 0.$$

Range: $\{y \in \mathbb{R} \mid y \neq 0\}$.

Answer: $D(f) = \left\{x \in \mathbb{R} \mid x \neq \frac{1}{2}\right\} = \left(-\infty, \frac{1}{2}\right) \cup \left(\frac{1}{2}, +\infty\right)$

$$R(f) = \{y \in \mathbb{R} \mid y \neq 0\} = (-\infty, 0) \cup (0, +\infty).$$

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