# F(x) = x2-7 and g(x) = x- 3, find (f º g )(x) [2]

• MHB
• trevor
In summary, the function (f º g)(x) is used to find the composition of two functions, f(x) and g(x). To find the composition, you need to plug the inner function (g(x)) into the outer function (f(x)). To plug in values for x, evaluate the inner function using the given value for x and then plug the result into the outer function. The order of functions in a composition can be rearranged, but the resulting function may be different. To solve for (f º g)(2), evaluate g(2) and then plug that value into f(x).
trevor
Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)

trevor said:
Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)

Hi trevor. What have you tried so far? :)

Joppy said:
Hi trevor. What have you tried so far? :)

I am clueless

(f o g)(x) means f(g(x)). That means, you replace the value in f(x) with g(x), thus your x2 - 7 will become (g(x))2 - 7. Can you continue from here?

## 1. What is the purpose of the function (f º g)(x)?

The purpose of the function (f º g)(x) is to find the composition of two functions, f(x) and g(x). This means that the output of g(x) is used as the input for f(x), resulting in a new function.

## 2. How do I find the composition of two functions?

To find the composition of two functions, you need to plug the inner function (g(x)) into the outer function (f(x)). In this case, (f º g)(x) = f(g(x)).

## 3. How do I plug in values for x in a composition of functions?

To plug in values for x in a composition of functions, you need to first evaluate the inner function (g(x)) using the given value for x. Then, take the result and plug it into the outer function (f(x)) to get the final output.

## 4. Can I rearrange the order of the functions in a composition?

Yes, the order of the functions can be rearranged in a composition. However, the resulting function may be different depending on the order of the functions.

## 5. How do I solve for (f º g)(2) in this given function?

To solve for (f º g)(2), first evaluate g(2) to get a specific value. Then, plug that value into f(x) to get the final output. In this case, (f º g)(2) = f(g(2)) = f(-1) = (-1)^2 - 7 = -6.

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