Question

Today I did a practice SAT problem.

If the function ƒ is defined by ƒ(x) = 2x + 3, and if ƒ(a) = 11, what is the value of a?

A. 4
B. 7
C. 11
D. 17
E. 25

This is the correct answer and the explanation

Here's Why:

If the function ƒ is defined by ƒ(x) = 2x + 3, and ƒ(a) = 11, then ƒ(a) = 2a + 3 = 11. Therefore, a = 11-3/2=4.

I don't understand the rules for functions. Why do you divide 11-3 by 2? Is there a specific formula you follow for them? Thanks for your help!

Answer 1

What they were doing is following the rules for 'solving equations'.

the notation
f(x) = 2x + 3 can be written also as
y = 2x + 3, it says the same thing
so when they say f(a) it means that whenever you saw an x has now been replaced by a,
so the 2x + 3 becomes 2a + 3
but you were told that this equals 11
so all you are doing is solving
2a + 3 = 11

Now recall your elementary rules of equations, "whatever you do to one side you must do to the other side"
so lets add -3 to both sides

2a + 3 - 3 = 11 - 3 (I wanted to get rid of +3)
2a = 8 ( I now want to get rid of the 2 in front of a)
divide both sides by 2
2a/2 = 8/2
a = 4