The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $\{R^{ - 1}\}$ is given by
The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $\{R^{ - 1}\}$ is given by
- A
$\{(2, 1), (4, 2), (6, 3).....\}$
- B
$\{(1, 2), (2, 4), (3, 6)....\}$
- C
${R^{ - 1}}$ is not defined
- D
None of these
Similar Questions
Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$, $f(3)=c$, $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$
Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$, $f(3)=c$, $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$
Let $f: N \rightarrow R$ be a function defined as $f(x)=4 x^{2}+12 x+15 .$ Show that $f: N \rightarrow S ,$ where, $S$ is the range of $f,$ is invertible. Find the inverse of $f$
Let $f: N \rightarrow R$ be a function defined as $f(x)=4 x^{2}+12 x+15 .$ Show that $f: N \rightarrow S ,$ where, $S$ is the range of $f,$ is invertible. Find the inverse of $f$
Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is
Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is
If $f : R \to R, f(x) = x^2 + 1$, then $f^{-1}(17)$ and $f^{-1}(-3)$ are
If $f : R \to R, f(x) = x^2 + 1$, then $f^{-1}(17)$ and $f^{-1}(-3)$ are
Which of the following function is invertible
Which of the following function is invertible