‹ Back to the paper
Consider the mapping is defined by such that is one-one onto. Based on the above information…
Consider the mapping $f: A \to B$ is defined by $f(x) = \frac{x-1}{x-2}$ such that $f(x)$ is one-one onto.
Based on the above information, answer the following questions by choosing the correct option.
(i)[2.0]
Domain of $f(x)$ is:
- (a)$\mathbb{R} - \{2\}$
- (b)$\mathbb{R}$
- (c)$\mathbb{R} - \{1, 2\}$
- (d)$\mathbb{R} - \{0\}$
(ii)[2.0]
Range of $f(x)$ is:
- (a)$\mathbb{R} - \{2\}$
- (b)$\mathbb{R}$
- (c)$\mathbb{R} - \{1\}$
- (d)$\mathbb{R} - \{0\}$
(iii)[2.0]
If $g(x) = 2f(x) - 1$, then $g(x)$ in terms of $x$ is:
- (a)$\frac{x+2}{x}$
- (b)$\frac{x+1}{x-2}$
- (c)$\frac{x-2}{x}$
- (d)$\frac{x}{x-2}$
(iv)[2.0]
A function $f(x)$ is said to be one-one if:
- (a)$f(x_1) = f(x_2) \implies x_1 = x_2$
- (b)$f(-x_1) = f(-x_2) \implies -x_1 = x_2$
- (c)$f(x_1) = f(x_2) \implies -x_1 = x_2$
- (d)$-f(x_1) = f(x_2) \implies x_1 = x_2$
Answer
No answer yet.
From ISC 2022 Specimen Mathematics Paper 1, question 23.