This may look complicated, but just follow the directions. You know that g(x) = 5x + 2. You also know
that = 6. First, get rid of the square root by squaring both sides. Now you have g = 36. Usually
there’s an x inside the parentheses. Treat this the same. This statement says that g of some number equals
- We also know that g of some number is the same as 5x + 2. So 5x + 2 = 36.
Simplify and you get . Careful, you’re not done. You now know that = , so a = , or (D).
Another way the SAT can make functions more complicated is to give you two functions to deal with
together. If you approach these problems one piece at a time, they will be easier to handle.
Here’s an example:
15.If f(g(a)) = 6, f(x) = + 2, and g(x) = |x^2 – 10|, which of the following is a possible value
of a ?
A)
B) 2
C) 6
D) 18Here’s How to Crack It
This is a great opportunity to plug in the answers! Take one of the middle answer choices and plug it in
for a, then work the problem one step at a time to see if f(g(a)) = 6. Try (B): If a = 2, then g(a) = |(2)^2 –
10| = |4 – 10| = |–6| = 6. So, f(g(a)) = f(g(2)) = f(6) = + 2 = 3 + 2 = 5. Since the problem states that
f(g(a)) is supposed to equal 6, (B) is not correct.
If you don’t know which way to go next, just pick a direction. Try (A): If a = , then g(a) = |( )^2 – 10|
= |2 – 10| = |–8| = 8. So, f(g(a)) = f(g( )) = f(8) = 2 = 4 + 2 = 6. Choice (A) is correct.
Sometimes the SAT will use a word problem to describe a function, and then ask you to “build a function”
that describes the real-world situation.