


Evaluating Functions
Evaluating a function simply means finding f(x)
at some specific value x. The Math IIC will likely
ask you to evaluate a function at some particular constant. Take
a look at the following example:

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 IIC may also ask questions in which you are asked
to evaluate a function at a variable rather than a constant. For
example:

To solve problems of this sort, follow the same method
you did 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
just like any other quantities. There are a few rules that help
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)
= x^{2} + 5 and g(x)
= x^{2} +
2x + 1: (f – g)(x) = x^{2} + 5 – x^{2} – 2x – 1 = –2x + 4 

Multiplication  If f(x)
= x and g(x)
= x^{3} +
8: (f g)(x) = x (x^{3} + 8) = x^{4} + 8x 

Division  If f(x)
= 2 cos x, and g(x)
= 2 sin^{2} x: 
As usual, when dividing, you have to be aware of possible
situations where 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 wherever the function in the
denominator equals zero.
