# Calculating g(f(5)) for Composite Functions

• ghostbuster25
In summary, the conversation is about solving for g(f(5)) using the given equations f(x) = x^2 - 3x and g(x) = 8 + 2x - x^2, with the restriction that x is greater than or equal to 1. The speaker initially finds f(5) to be 10, but when attempting to find g(10), they get a negative number of -72, which they realize cannot be correct due to the restriction on the function g. The conversation concludes with the speaker understanding the difference between the restriction on the domain of x and the actual values that the function g can output.
ghostbuster25
Im looking for g(f(5))

where f(x) = X^2 - 3x

and g(x) = 8 + 2x - x^2 xER and x is greater than or equal to 1

I have first found f(5)
(5)^2-3(5)
which equals 10

However when i do g(10)
8+2(10)-(10)^2

that gives me a negative number of -72! Which can't be right because g has to greater than or equal to 1

Where am i going wrong?

No. What you said was that x has to be $\geq 1$, not g. There is a difference - can you tell me what the difference is?

cyby said:
No. What you said was that x has to be $\geq 1$, not g. There is a difference - can you tell me what the difference is?

is it because g is a gunction of x, not x itself!? am i doing it correctly then? :)

The difference is that you're limiting the *domain* of g to be positive. This said nothing about the function must evaluate to.

What this is essentially saying is that g(1) is ok, but g(0.5) isn't, because 0.5 is < 1.

Everything else looks good.

ahhh yer that makes sense :) thanks

## 1. What is a composite function?

A composite function is a combination of two or more functions where the output of one function is used as the input for the other function. It is denoted as f(g(x)) and read as "f of g of x".

## 2. How do you calculate g(f(5))?

To calculate g(f(5)), you first need to find the value of f(5) by plugging in 5 as the input for the function f. Then, take this value and use it as the input for the function g. The resulting output will be the value of g(f(5)).

## 3. Can you give an example of calculating g(f(5))?

Sure, let's say we have the functions f(x) = 2x + 3 and g(x) = x^2. To find g(f(5)), we first calculate f(5) which is 2(5) + 3 = 13. Then, we use this value as the input for g, giving us g(13) = 13^2 = 169. Therefore, g(f(5)) = 169.

## 4. What is the significance of calculating g(f(5))?

Calculating g(f(5)) allows us to evaluate the composition of functions, which can be useful in real-world applications like in physics and economics. It also helps us understand the relationship between different functions and how they affect each other.

## 5. Is there a specific order in which functions should be composed?

Yes, the order of composition matters. In general, f(g(x)) is not equal to g(f(x)). This is known as the "order of operations" for composite functions. When working with composite functions, it is important to pay attention to the order in which the functions are written.

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