Question

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

f(x)= 1/(5x-6)

Answer 1

Answer on Question # 76192 – Math – Discrete Mathematics

Question

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

$$f(x) = 1/(5x-6)$$

Solution

Given, $f(x) = 1/(5x-6)$.

The domain does not contain the values for $x$ that make the given expression undefined:

$$5x-6 = 0$$

or,

$$x = 6/5$$

The domain in this problem is all values of $x$ that make the expression defined.

Hence domain:

$$(-\infty, 6/5) \cup (6/5, \infty) = \{x \mid x \neq 6/5\}.$$

The range is the set of all valid $y$ values:

$$(-\infty, 0) \cup (0, \infty) = \{y \mid y \neq 0\}$$

Answer: the domain is $(-\infty, 6/5) \cup (6/5, \infty)$, the range is $(-\infty, 0) \cup (0, \infty)$.

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