You know those Russian nesting dolls? Each doll has a
smaller and smaller doll inside it? Compound functions are like
that. A compound function is a function that operates on another
function. It’s written out like this: f(g(x)).
To evaluate a compound function, first evaluate the internal function, g(x).
Next, evaluate the outer function at the result of g(x).
It’s just double substitution: a classic SAT question that looks
much meaner than it really is.
Try this example on for size:
= x2 + 2x and j(x)
= | + 2|. What is j(h(4))?
First evaluate h(4):
Now plug 24 into the definition of j:
Just make sure you pay attention to the order in which
you evaluate the compound function. Always evaluate the inner function
first. If the question had asked you to evaluate h(j(4)),
you’d get a completely different answer:
As with ordinary evaluating functions questions, the SAT
doesn’t always give you a constant with which to evaluate compound
= 3x + 1 and g(x)
= . What is g(f(x))?
When you aren’t given a constant, just substitute the
definition of f(x) as
the input to g(x). It’s
as if you’re being asked to evaluate a signle function at a variable
rather than a constant.
Compound Wacko Symbols Questions
The SAT also sometimes asks compound symbols questions.
These are exactly the same as compound function questions.
||Let a#b#c#d be
defined for all numbers by a#b#c#d = ab – cd. If x =
6#3#5#4, then what is the value of 7#x#3#11?
Strange symbols are flying all over the place, and the
question is asking you to calculate the value of a strange symbol
with a variable in it?! No problem. The answer to this question
is only two steps away:
Calculate the value of x.
the value of 7#x#3#11 (which won’t
be very hard, since by step 2, you’ll know exactly
what x equals).
Now plug x = –2 into 7#x#3#11: