FUNCTIONS AND INVERSES

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FUNCTIONS AND INVERSES

• A ONE-TO-ONE FUNCTION
• A TWO-TO-ONE FUNCTION
• AN EXPONENTIAL FUNCTION
• THE PRINCIPAL SINE FUNCTION
• THE PRINCIPAL COSINE FUNCTION
• THE PRINCIPAL TANGENT FUNCTION
• EXAMPLE

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A ONE-TO-ONE FUNCTION
Y
4
y x 1
3
x y - 1
2
1
-1
-2
X
1
2
3
4
-1
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A TWO-TO-ONE FUNCTION
Y
4
3
y x2
2
x vy
1
X
1
2
3
4
-1
-2
-3
-4
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AN EXPONENTIAL FUNCTION
Y
4
3
y 2x
2
x log2y
1
X
1
2
3
4
-1
-2
-3
-4
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THE SINE FUNCTION
Y
y sin x
1
y
X
x
pi/2
pi
3pi/2
2pi
-pi/2
-pi
-3pi/2
-2pi
-1
x arcsin y
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PRINCIPAL SINE FUNCTION
Since the principal sine function Sin is
one-to-one, it has an inverse Sin-1 , also
called Arcsin or arcsin.
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THE COSINE FUNCTION
y cos x
y
X
x
pi/2
pi
3pi/2
-2pi
-pi/2
-pi
-3pi/2
x arccos y
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PRINCIPAL COSINE FUNCTION
Since the principal sine function Cos is
one-to-one, it has an inverse Cos-1 , also
called Arccos or arccos.
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THE TANGENT FUNCTION
Y
y tan x
y
1
X
pi/2
pi
-pi/2
-pi
x
-pi/4
pi/4
-1
x arctan y
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PRINCIPAL TANGENT FUNCTION
Since the principal tangent function Tan is
one-to-one, it has an inverse Tan-1 , also
called Arctan or arctan.
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EXAMPLE