The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $\{R^{ - 1}\}$ is given by
$\{(2, 1), (4, 2), (6, 3).....\}$
$\{(1, 2), (2, 4), (3, 6)....\}$
${R^{ - 1}}$ is not defined
None of these
If $a * b=10$ ab on $Q^{+}$ then find the inverse of 0.01
Let $f: N \rightarrow Y $ be a function defined as $f(x)=4 x+3,$ where, $Y =\{y \in N : y=4 x+3$ for some $x \in N \} .$ Show that $f$ is invertible. Find the inverse.
Let $f : R \rightarrow R\ f(x) = x^3 -3x^2 + 3x\ -2$ , then $f^{-1}(x)$ is given by
If $f:IR \to IR$ is defined by $f(x) = 3x - 4$, then ${f^{ - 1}}:IR \to IR$ is
Show that $f:[-1,1] \rightarrow R ,$ given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$
$($ Hint: For $y \in $ Range $f$, $y=f(x)=\frac{x}{x+2}$, for some $x$ in $[-1,1]$, i.e., $x=\frac{2 y}{(1-y)})$