Inverse & Inverse Trig Functions Worksheet - Math141e, Pennsylvania State University Page 6
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6Calculus Maximus
WS 2.8: Inverse & Inverse Trig Functions
_____ 17. Let f be a twice-differentiable function and let g be its inverse. Consider the following
equations:
(
)
(
)
( )
( )
= ,
=
I.
g f x
x
f g x
x
(
)
(
)
(
)
( )
( )
2
( )
( )
′′
′
′
′′
+
=
II.
f
g x
g x
f g x g x
0
1
( )
′
=
III.
g x
(
)
( )
′
f g x
Which of the three above do both f and g satisfy?
(A) I and III only
(B) I only
(C) III only
(D) I and III only
(E) I, II, and III
π
π
( )
( )
g ′
=
−
≤ ≤
_____ 18. Find the value of
1
when g is the inverse of the function
f x
2sin
x
,
x
.
2
2
1
1
1
−
−
(A)
(B) 1
(C)
(D)
(E) 1
3
2
3
1
( )
( )
=
=
_____ 19. Suppose g is the inverse function of a differentiable function f and
. If
G x
f
3
7
( )
g x
1
( )
( )
f ′
G ′
= , find
and
3
7
.
9
−
−
−
(A) 5
(B) 4
(C) 6
(D) 1
(E) 4
dy
(
)
−
=
_____ 20. Find
when
(Preview your answer choices first. Notice there is no trig!)
tan 2
x y
2
x
dx
2
dy
8
x
=
(A)
2
+
dx
1 4
x
2
dy
8
x
= −
(B)
2
+
dx
1 4
x
2
dy
4
y
= −
(C)
2
dx
+
2
x
2
dy
4
y
=
(D)
2
+
dx
2
x
2
dy
8
x
= −
(E)
2
+
dx
1 4
y
Page 6 of 6
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