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Other
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
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Topic:
Functions and Logarithms (Math Problem Sample)
Instructions:
This was a quiz for mathematical functions and logarithms. There were five questions, requiring algebraic and graphical solutions. Each step was carefully listed and a graph was drawn for the inverse function before being superimposed on the original function graph. Similarly, the logarithmic questions were solved using logarithm properties. source..
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Quiz # 9
Q1.
f (x) =
x
+
4
Yes. Using the horizontal line test, we see that every point of the graph intersects with the line once.
545428528945CaptionCaption
(d)
f

1
(x) is obtained by making x the subject of the formula. So, as y =
x
+
4
, we get by squaring both sides,
y
2
=
x
+
4
x
=
y
2

4
,
Interchanging y for x, we get,
f

1
(x) =
x
2

4
for x > 0.
e)
Q2.
Given
f
(
x
)
=
(
2
x
+
1
)
/
(
x

3
)
, we can write this as
y
=
(
2
x
+
1
)
/
(
x

3
)
by letting
f
(
x
)
=
y
.
So, by making
x
the subject of the formula, we get,
y
(
x

3
)
=
2
x
+
1
y
x

3
y
=
2
x
+
1
y
x

2
x
=
1
+
3
y
x
(
y

2
)
=
1
+
3
y
x
=
(
1
+
3
y
)
/
(
y

2
)
So, by knowing that
x
=
f

1
(
y
)
We get,
f

1
(
x
)
=
(
1
+
3
x
)
/
(
x

2
)
.
Q3.
B, D, A, C (As you go down)
L: (0, 2) M: (1, 0) N: (10/9, 0) O: (0, 9/2)
Q4.
y
=
...
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