GRAPH OF ONE-TO-ONE FUNCTION

UR QUESTIONS, OUR SOLUTION: 3

How a one-to-one function looks like on cartesian plane ? ( DC/M)
( asked by RAVI JHA)

SOLUTION: One-to-one functions has unique mapping, that is for a unique value of x we will have unique value of y. All functions which are strictly increasing or strictly decreasing in their domain will be one-one functions.

Otherwise, they will be many-one.

For eg: y = x, y = log(x), y = e(x) are all strictly increasing function they will be one-to-one.

y = -x , y =e(-x) are strictly decreasing functions they will also be one-to-one.

whereas, y= sin(x) , y = |x|, y = x(sq), y= cos(x), y = tan(x) will all be many-one functions because their graph is decreasing for some values of x and increasing for others.

Note: e(x) is e raise to x, e(-x) is e raise to -x, x(sq) is x sqaure