Evaluating Functions
Evaluating a function simply means finding f(x)
at some specific value x. The Math IC will likely
ask you to evaluate a function at some particular constant. Take
a look at the following example:
|
|
|
If f(x)
= x2 – 3, what is f(5)? |
|
Evaluating a function at a constant involves nothing more
than substituting the constant into the definition of the function.
In this case, substitute 5 for x:
It’s as simple as that.
The Math IC may also ask questions in which you are asked
to evaluate a function at a variable rather than a constant. For
example:
|
|
|
If f(x)
= 3x/
4–x,
what is f(x + 1)? |
|
To solve problems of this sort, follow the same method
you used for evaluating a function at a constant: substitute the
variable into the equation. To solve the sample question, substitute
(x + 1) for x in the definition
of the function:
Operations on Functions
Functions can be added, subtracted, multiplied,
and divided like any other quantity. There are a few rules that
make these operations easier. For any two functions f(x)
and g(x):
|
Rule |
Example |
| Addition |
 |
If f(x)
= sin x, and g(x)
= cos x:
(f + g)(x)
= sin x + cos x |
| Subtraction |
 |
If f(x)
= x2 + 5, and g(x)
= x2 + 2x +
1:
(f – g)(x)
= x2 + 5 – x2 –
2x – 1 = –2x + 4 |
| Multiplication |
 |
If f(x)
= x, and g(x)
= x3 + 8:
 |
| Division |
 |
If f(x)
= 2 cos x, and g(x)
= 2 sin2 x:
 |
As usual, when dividing, you have to be aware of possible
situations in which you inadvertently divide by zero. Since division
by zero is not allowed, you should just remember that any time you
are dividing functions, like f(x)⁄g(x),
the resulting function is undefined whenever the function in the
denominator equals zero.
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