Ap Calculus Derivatives Of Inverse Functions Worksheet Page 4
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1
2
3
4
π
π
d
1
2
2
3
1
9.
Given
on the interval
,
h
(
x
)
sin
x
,
h
2
2
dx
3
3
x
1
2
h
'
6
10.
��
−3
−1
1
4
−3
g(x)
5
1
0
1
1
g’(x)
−4
−2
5
6
1
1
a)
g
1
5
g
'
1
1
1
1
b)
g
3
g
'
4
2
11.
��
−1
0
2
4
−5
−1
h(x)
4
7
1
1
h’(x)
3
5
2
6
1
f
'
1
2
a)
h
'
0
1
f
'
4
6
b)
h
'
2
1
12. If
f
(x
)
is an even function, then
f
(
x
)
exists.
FALSE. An even function has symmetry with respect to the y-axis and, therefore, cannot be one-
to-one.
-1
13. If the inverse of f exists, then the y-intercept of f is an x-intercept of f
.
TRUE. Switching x and y coordinates will result in switching x and y intercepts.
n
1
14. If
f
(
x
)
x
where n is odd, then
f
(
x
)
exists.
where n – 1 is even. So
n
n
1
TRUE. If
where n is odd, its derivative is
f
(
x
)
x
f
( '
x
)
nx
n
for all values of x except x = 0. Therefore
f
(
x
)
x
is strictly monotonic.
f
( '
x
)
0
-1
15. There exists no function f such that f = f
.
FALSE. There are many such functions! Some examples: �� = ��, �� = −��, �� = −�� + ��,…
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