Q.Find the possible domains for which the following are one to one functions
a) y = x^2
b) y= x(x-2)
c) y = 2x-3
i kno the for a 1-1 function there is max and min of the 1 y-value for every x-value and vice-versa
all i need is now are the answers and the explanations to the answers.
for eg i for b) i know that domain: x<=0 or x>=1 but why not x<=0 or x>=2
i am so damn confused, please help me thank you
a one to one function satisfies the horizontal line test. so drawing any horizontal line should cut the graph at only one point. for quadratics, this happens only when our curve does not pass the axis of symmetry, since if it does, it will be increasing on both sides of the axis and a horizontal line will touch it twice