I was hoping I could get some help with a homework question.
"Draw the graph of f. State whether f is One to One and also whether it is Onto."
Equation 1 : f(x) = 1/x^2 if x≤-1
Equation 2 : f(x) = (x+3)/2 if -1≤x≤1
Equation 3 : f(x) = 2 + (1/x) if x≥1
The Attempt at a Solution
I know it isn't Onto because it doesn't use all of the elements in the codomain, but I can't tell whether it's One To One.
All of the examples we've done in class have multiple domain elements mapped to single codomain elements (A and C mapped to B). We haven't done anything with single domain elements mapped multiple codomain elements (A mapped to B and C).
"One To One" suggests that A can only map to one value of B, and B can only map to one value of A. So in this question we have one value of A mapped to multiple values of B, which makes me think that the function f in this case is neither One To One nor Onto.
But I get caught out by things like this all the time.
Could anyone help me, please. I'd really appreciate it.
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