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SAT (Fall 2023)
Course: SAT (Fall 2023) > Unit 10
Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example
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Function notation — Basic example
Watch Sal work through a basic Function notation problem.
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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?(20 votes)
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.(40 votes)
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?(18 votes)
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) .(25 votes)
I am struggling to understand this question.(7 votes)- hello bro, hows life?(6 votes)
- I cannot understand what the question is asking:((7 votes)
why do you have to replace g where x is(0 votes)
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.(12 votes)
I'm still confused on what f(x) means. Does it mean f times the variable?(3 votes)
It means function.
Here are the function lessons on Khan Academy: https://www.khanacademy.org/math/algebra/algebra-functions(3 votes)
- i dont freaking understand(4 votes)
- what yo. What is this asking g(2 votes)
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.(4 votes)
Video transcript
- [Instructor] We're told the table above shows some values of
the functions F and G. For which value of X is F of X minus G of X equal to X? Pause this video and see
if you can figure this out. All right, so they give
a bunch of X values and for each of those X values we see, for example, when X
equals zero what F of zero is and we see what G of zero is. Now we need to figure out when F of X minus G of X is equal to X, or another way to think about it, when the number here minus the number here is equal to the number right over there. So let's just try them out. What's nine minus negative nine? Well, that would be positive 18, not zero. So we can rule that one out. What's eight minus negative seven? Well, that would be positive 15, not one. We can rule that out. What's five minus negative five? Well, that would be positive 10, not two. Rule that out. What is zero minus negative three? Well, that's going to be positive three, which is what X was right over here. So that's the answer. That's the value of X for which F of X minus G of X is equal to X. It's three. We can verify for four. Let's see, F of four is negative seven. So negative seven minus negative one is going to be negative seven plus one, which is negative six, not four. So yeah, we like that choice.