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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Functions

NDA 2020 · Mathematics · Functions

Which one of the following is correct in respect of the graph of...

Which one of the following is correct in respect of the graph of y=1x−1y=\frac{1}{x-1} ?

Options

  1. AThe domain is {x∈R∣x≠1}\{x \in \mathbb{R} \mid x \neq 1\} and the range is the set of reals.
  2. BThe domain is {x∈R∣x≠1}\{x \in \mathbb{R} \mid x \neq 1\}, the range is {y∈R∣y≠0}\{y \in \mathbb{R} \mid y \neq 0\} and the graph intersects yy-axis at (0,−1)(0,-1).
  3. CThe domain is the set of reals and the range is the singleton set {0}\{0\}.
  4. DThe domain is {x∈R∣x≠1}\{x \in \mathbb{R} \mid x \neq 1\} and the range is the set of points on the yy-axis.

Correct answer

B. The domain is {x∈R∣x≠1}\{x \in \mathbb{R} \mid x \neq 1\}, the range is {y∈R∣y≠0}\{y \in \mathbb{R} \mid y \neq 0\} and the graph intersects yy-axis at (0,−1)(0,-1).

Step-by-step solution

Given graph Y=1x−1Y=\frac{1}{x-1} This is defined for all real xx, except x=1x=1. Range of the graph is y∈R∣y≠0y \in \mathbb{R} \mid y \neq 0 Table for the graph :
Graph of function -
Thus, graph intersect yy-axis at (0,−1)(0,-1).
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