The functions which map [-1, 1] to [0, 2] are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) linear function is of the form $f(x) = ax + b$. We want to map the interval $[-1, 1]$ to $[0, 2]$. Case $1$: $f(-1) = 0$ and $f(1) = 2$. $-a + b =

Vedclass · Accepted Answer

Two linear functions

Vedclass · Answer

(B) linear function is of the form $f(x) = ax + b$. We want to map the interval $[-1, 1]$ to $[0, 2]$. Case $1$: $f(-1) = 0$ and $f(1) = 2$. $-a + b = 0 \implies a = b$. $a + b = 2 \implies 2a = 2 \implies a = 1, b = 1$. So,$f(x) = x + 1$. Case $2$: $f(-1) = 2$ and $f(1) = 0$. $-a + b = 2$. $a + b = 0 \implies b = -a$. $-a - a = 2 \implies -2a = 2 \implies a = -1, b = 1$. So,$f(x) = -x + 1$. Thus,there are two such linear functions.

The functions which map $[-1, 1]$ to $[0, 2]$ are

Similar Questions

Which of the following function$(s)$ is/are transcendental?

Let a function $f: (0, \infty) \to (0, \infty)$ be defined by $f(x) = |1 - \frac{1}{x}|$. Then $f$ is

If $f: R \rightarrow R$,such that $f(x)=\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}$,then $f$ is

Check the injectivity and surjectivity of the following function $f : N \rightarrow N$ given by $f(x) = x^{3}$.

The number of onto functions from the set $\{1, 2, \ldots, 11\}$ to the set $\{1, 2, \ldots, 10\}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module