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Precalculus Examples
Step-by-Step Examples
Precalculus
Operations On Functions
Find the Difference of the Two Functions
f
(
x
)
=
x
4
+
x
3
−
11
x
2
−
5
x
+
30
f
(
x
)
=
x
4
+
x
3
-
11
x
2
-
5
x
+
30
,
g
(
x
)
=
2
x
−
2
g
(
x
)
=
2
x
-
2
Step 1
Replace the
function
designators with the actual
functions
in
f
(
x
)
−
g
x
f
(
x
)
-
g
x
.
x
4
+
x
3
−
11
x
2
−
5
x
+
30
−
(
2
x
−
2
)
x
4
+
x
3
-
11
x
2
-
5
x
+
30
-
(
2
x
-
2
)
Step 2
Simplify each
term
.
Tap for more steps...
Step 2.1
Apply the
distributive property
.
x
4
+
x
3
−
11
x
2
−
5
x
+
30
−
(
2
x
)
−
−
2
x
4
+
x
3
-
11
x
2
-
5
x
+
30
-
(
2
x
)
-
-
2
Step 2.2
Multiply
2
2
by
−
1
-
1
.
x
4
+
x
3
−
11
x
2
−
5
x
+
30
−
2
x
−
−
2
x
4
+
x
3
-
11
x
2
-
5
x
+
30
-
2
x
-
-
2
Step 2.3
Multiply
−
1
-
1
by
−
2
-
2
.
x
4
+
x
3
−
11
x
2
−
5
x
+
30
−
2
x
+
2
x
4
+
x
3
-
11
x
2
-
5
x
+
30
-
2
x
+
2
x
4
+
x
3
−
11
x
2
−
5
x
+
30
−
2
x
+
2
x
4
+
x
3
-
11
x
2
-
5
x
+
30
-
2
x
+
2
Step 3
Simplify by adding
terms
.
Tap for more steps...
Step 3.1
Subtract
2
x
2
x
from
−
5
x
-
5
x
.
x
4
+
x
3
−
11
x
2
−
7
x
+
30
+
2
x
4
+
x
3
-
11
x
2
-
7
x
+
30
+
2
Step 3.2
Add
30
30
and
2
2
.
x
4
+
x
3
−
11
x
2
−
7
x
+
32
x
4
+
x
3
-
11
x
2
-
7
x
+
32
x
4
+
x
3
−
11
x
2
−
7
x
+
32
x
4
+
x
3
-
11
x
2
-
7
x
+
32
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