If polynomial function vanishes at
x
=
a
, then
(
x
−
a
)
must be one of its factors.
Thus
(
x
−
7
)
,
(
x
−
4
−
√
6
)
and
(
x
−
4
+
√
6
)
are factors of the required polynomial.
The simplest polynomial that satisfies this is
(
x
−
7
)
(
x
−
4
−
√
6
)
(
x
−
4
+
√
6
)
=
(
x
−
7
)
{
(
x
−
4
)
−
√
6
}
{
(
x
−
4
)
+
√
6
}
=
(
x
−
7
)
{
(
x
−
4
)
2
−
6
}
=
(
x
−
7
)
(
x
2
−
8
x
+
16
−
6
)
=
(
x
−
7
)
(
x
2
−
8
x
+
10
)
The answer to this question is ....................................
We actually don't need to do any computation. By definition, the inverse function 
changes the role of input and output. So, if a function f maps x onto y, the inverse function maps y onto x.
You have to think like this: if the function makes a step further, the inverse function makes that same step back.
This means that the composition 
is always the identity function 
. In fact,
So, for every function, you have
Numerical expressions contain numbers, while algebraic expressions contain variables and numbers.
<u>Numerical Expression</u>
"Difference" indicates that we'll be subtracting 13 from 48.
48 - 13 = 35
<u>Algebraic Expression</u>
Variables represent the unknown number, in this case the difference between 48 and 13. Let d represent the difference between the two.
48 - 13 = d
35 = d
