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WOLFRAM|DEMONSTRATIONS PROJECT

Is the Given Function Injective?

​
a
0.2
b
-0.36
x
1
0.2
x
2
0.8
x
1
≠
x
2
True
f(
x
1
) = f(
x
2
) False
A function
f
is injective (or one-to-one) if different inputs give different outputs. In symbols,
f
is injective if whenever
x
1
≠
x
2
, then
f(
x
1
)≠f(
x
2
)
. To show that a function is not injective, find
x
1
≠
x
2
such that
f(
x
1
)=f(
x
2
)
. Graphically, this means that a function is not injective if its graph contains two points with different
x
values and the same
y
value.
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