Describe the relationship between input and output values for composite functions

Evaluating composite functions: using tables (video) | Khan Academy

By combining these two relationships into one function, we have performed .. Explanation of the composite function. g(x), the output of g is Form a meaningful composition of these two functions, and explain what it means. . When working with functions given as tables, we read input and output values from the table. Describe the relationship of input and output values for composite functions. Explain how you know if a radical expression is in simplest. In mathematics, function composition is the pointwise application of one function to the result of The resulting composite function is denoted g ∘ f: X → Z, defined by (g ∘ f)(x) The composition of functions is a special case of the composition of relations, so all properties of the latter are true of composition of functions.

I wrote these small here so we have space for the actual values.

Evaluating composite functions: using tables

So first let's just evaluate, and if you are now inspired, pause the video again and see if you can solve it. Although, if you solved it the first time, you don't have to do that now.

What's g of zero? Well, when we input x equals zero, we get g of zero is equal to five. So g of zero is five. So that is five.

Evaluating composite functions: using graphs

So we're now going to input five into our function f. We're essentially going to evaluate f of five. So when you input five into our function. I'm gonna do it in this brown color. When you input x equals five into f, you get the function f of five is equal to So this is going to be So, f of g of zero is equal to Now, let's do g of f of zero. So now let's evaluate. I'll do this is different colors. G, maybe I'll use those same two colors actually. So now we're going to evaluate g of f of zero.

G of f of zero, and the key realization is you wanna go within the parenthesis. Evaluate that first so then you can evaluate the function that's kind of on the outside. So here we're going to take zero as an input into the function f, and then whatever that is, that f of zero, we're going to input into our function g.

We're going to input into our function g, and what we're going to be, and then the output of that is going to be g of f of zero. So, let's see, what is f of zero?

You see over here when our input is zero, this table tells us that f of zero is equal to one. So f of zero is equal to one. What does all this mean?

Describe the relationship of input and output values for composite functions. - Science Mathematics

We just have to remind ourselves what functions are all about. They take an input and they give you an output. So really, what we're doing is we're going to take, we have the function f. We have the function f.

Evaluating composite functions: using graphs (video) | Khan Academy

We're going to input negative five into that function. We're going to input negative five into that function and it's going to output f of negative five. It's going to output f of negative five and we can figure what that is. And then that's going to be the input into the function g. So that's going to be the input into the function g and so we're going to, and then the output is going to be g of f of negative five, g of f of negative five.

Let's just do it step by step. So the first thing we wanna figure out is what is the function f when x is equal to negative five? What is f of negative five?

  • What is the relationship of input and output values for composite functions?
  • Composing functions
  • Relationship of Input and Output values of Composite Functions. How would you evaluate f(g(x)?

Well we just have to see when x is equal to negative five. When x is equal to negative five, the function is right over here. Let's see, let me see if I can draw a straight line. So then x is equal to negative five. The function is right over here.