Algebra Equations Worksheets With Answer Keys Page 20
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20Chapter 5
20
( )
( )
x
f x =
=
x > .
10. The function
10
has inverse function
g x
log
x
with
0
1
( )
′
=
(a) Show that
g x
.
(
)
′
f g x
( )
( )
( )
( )
( )
1
′
′
=
x
=
x
f
x
ln10 10
+1
f
x
ln10 10
( )
′
=
g x
( )
ln 10
x
(
)
(
) (
)
(
)
′
′
=
=
g x
( )
+1
f g x
( )
ln10
x
f g x
( )
ln10 10
1
(
)
1
=
( )
=
log
x
ln10 10
′
=
+1 Show
g x
(
)
′
f g x
( )
(
)
′
f g x
( )
(
)
=
ln10
x
(b) What is the area of the region between f and g on the interval
[ ]
1, 2 ?
+1 limits of integration
2
∫
(
)
−
=
f x
( )
g x dx
( )
38.919
+1 integrand
+1 38.919
1
( )
x = ?
(c) What is the equation of the tangent line of g at
4
g ′
≈
+1
4
0.109
( )
g ′
=
+ 1
m
4
1
1
( )
′
=
=
+
g x
y
x b
b =
+1
0.168
(
)
(
)
ln10
x
ln10 4
1
1
( )
( )
′
=
=
+
g
4
log 4
4
b
(
)
(
)
ln10 4
ln10 4
≈
0.109
1
=
−
b
log 4
ln10
≈
0.168
⎛
⎞
1
1
=
+
−
y
x
log 4
⎜
⎟
(
)
ln10 4
⎝
ln10
⎠
=
+
0.109
x
0.168
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