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Mathematics
One-one function
Let $X=\left\{ a,b,c,d \right\}$ then one-one mapping $f:X\to X$ such that $f\left( a \right)=a,f\left( b \right)\ne b,f\left( d \right)\ne d$ are given by
1. $\left\{ \left( a,a \right),\left( b,c \right),\left( c,d \right),\left( d,b \right) \right\}$
2. $\left\{ \left( a,a \right),\left( b,d \right),\left( c,c \right),\left( d,b \right) \right\}$
3. $\left\{ \left( a,a \right),\left( b,d \right),\left( c,b \right),\left( d,c \right) \right\}$
A. Only (1) is true.
B. (1) and (2) is true.
C. (1), (2) and (3) are true.
D. Only (3) is true.
Mathematics
One-one function
The number of one-one functions that can be defined from set {a, b, c, d} to the set {1, 2, 3, 4} is?
Mathematics
One-one function
Number of one-one functions from A to B where n(A)= 4 and n(B)= 5.
a). 4
b). 5
c). 120
d). 90

Mathematics
One-one function
What are vertical and horizontal line tests for 1-1 function?

Mathematics
One-one function
Find the interval for which $f\left( x \right)=\sin x$ is one-one $\left[ 0,\pi \right]$
Mathematics
One-one function
How do you use the horizontal line test to determine whether the function $g\left( x \right)={{\left( x+5 \right)}^{3}}$ is one to one?

Mathematics
One-one function
Define many-one function. Give an example of many-one functions.

Mathematics
One-one function
How do you use the horizontal line test to determine whether the function $g\left( x \right)=\dfrac{4-x}{6}$ is one to one?

Mathematics
One-one function
How do you use the horizontal line test to determine whether the function $g\left( x \right)=\dfrac{4-x}{6}$ is one to one?

Mathematics
One-one function
Let $A = \left\{ {1,2,3} \right\},B = \left\{ {4,5,6,7} \right\}$ and let $f = \left\{ {\left( {1,4} \right),\left( {2,5} \right),\left( {3,6} \right)} \right\}$ be a function from A to B. State whether f is one-one.

Mathematics
One-one function
Let f be a one – one function with domain {x, y, z} and range {1, 2, 3}. It is given that exactly one of the following statements is true and the remaining two are false, $f\left( x \right)=1,f\left( y \right)\ne 1,f\left( z \right)\ne 2$. Determine, ${{f}^{-1}}\left( 1 \right)$.

Mathematics
One-one function
Show that the function $f\left( x \right)=\dfrac{4x+3}{6x-4}$ defined in $A=R-\left\{ \dfrac{2}{3} \right\}$. Show that f(x) is one-one and onto and hence find ${{f}^{-1}}$

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