SAT SUBJECT TEST MATH LEVEL 1

FUNCTIONS

CHAPTER 15
Functions and Graphs

COMBINING FUNCTIONS

If f and g are two functions with overlapping—possibly equal—domains, then for all numbers x that are in both domains, it is possible to define the sumdifferenceproduct, and quotient of f and g.

Key Fact N5

If x is in the domain of both f and g:

• (f + g)(x) = f (x) + g(x)

• (f – g)(x) = f (x) – g(x)

• (fg)(x) = f (x) • g(x)

• 

The only way KEY FACT N5 comes up on the Math 1 test is in evaluating the combination of two functions or in simplifying a quotient. If you need to evaluate the combination of functions, don’t actually combine them; use KEY FACT N5.

EXAMPLE 10: Let f (x) = 3x + 5 and g (x) = x2 + x – 5. To evaluate (fg)(2), you could first multiply f (x) • g (x):

f (x)g(x) = (3x + 5)(x2 + x – 5) = 3x 3 + 8x2 – 10x – 25

and then plug in x = 2:

3(23) + 8(22) – 10(2) – 25 = 24 + 32 – 20 – 25 = 11

but you shouldn’t. Instead you should evaluate first and then multiply:

(fg)(2) = f (2)g(2) = (3(2) + 5)(22 + 2 – 5) = (11)(1) = 11.

EXAMPLE 11: If f (x) = (x2 + x – 2), g (x) = (x2 – x – 2), h(x) = (x2 – 1), and x  1, –1, then: