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### Course: Digital SAT Math>Unit 8

Lesson 5: Nonlinear functions: medium

# Function notation — Basic example

Watch Sal work through a basic Function notation problem.

## Want to join the conversation?

• What exactly does something like "f of g of x mean?" Not in terms of values, but in terms of operations. What exactly does it mean?
• If I'm not mistaken it means f(g(x)) and it is normally written as (f o g)(x) or in this case you can write the function (g o f)(x). This is a Function Composition that is applying one function , f(x), to the results of another, g(x). X is an "input" and you plug in what is necessary for x, then you plug that value into g, simplify, and then plug the result into f. I hope this helps.
• Can't we solve this problem without having a look at the answer choices? What if this were a grid-in question or a question on a non-SAT paper? How can we solve this?
• Yes, it can be solved without substitution as :

f(g(x)) = f(x^2 - 5) = square root of (x^2 + 4)

Let y = x^2 -5 which implies x^2 = y + 5
Then,
f(y) = square root of (y + 5 + 4)
= square root of (y + 9)

Since y is a variable, we can replace it with x which gives f(x) = square root of (x + 9) .
• I am struggling to understand this question.
• hello bro, hows life?
• I cannot understand what the question is asking:(
• ur selling
• why do you have to replace g where x is
• If I had f(x) = x^2 + x + 1, and I wanted to calculate f(3), I replace all the x's with 3's, and I get 3^2 + 3 + 1, which is 9 + 3 + 1 or 13.
Same way, If g(x) = x + 1, I wanted to calculate f(g(x)), I replace all the x's with g(x)'s, and I get g(x)^2 + g(x) + 1, which is (x + 1)^2 + (x + 1) + 1. Evaluating (x + 1)^2 gives us x^2 + 2x + 1 + x + 1 + 1, and simplifying leaves x^2 + 3x + 3 as our answer.
• I'm still confused on what f(x) means. Does it mean f times the variable?
• what yo. What is this asking g
(1 vote)
• This question is asking us to do something with the table of values to find a certain value that the question is asking for. We have three columns in our table. X, f(x), and g(x). f(x) and g(x) represent the output of functions f and g. That is to say, they are what you get when you apply a certain rule ("f" or "g") to x.
Now, we want to find the value of x for which f(x) - g(x) = x. The easiest way to do this is to calculate f(x) - g(x), or the 2nd column minus the third column, for each row.
Going down the rows, we get 18, 15, 10, 3, and -6. The only one of these f(x)-g(x) values that is the same as the corresponding x value is 3, so 3 is our answer.