f f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to (f circle g) (10)?

Answer 1

Hi Tamese,

Your question is an example of a composition of functions,which is pronounced f-compose-g of x.

The way to think about these types of questions is that you can replace the x in the F(x) function with the expression or value of g(x).

Also, another way to write this problem is:

( f o g)(x) = f(g(x))

Let's get to solving!

So f(x)=x^2+1 and g(x)=x-4 and we want to solve for f(g(10).

There are two ways to think about solving:

Option1:

"Working inside out"

First, solve for the innermost functions value and plug it into the function that wraps it. In our case solve for g(x) where x=10 then solve for f(x) with x =g(10).

g(10)= 10-4

g(10)=6

Next we solve for f(g(10)), since g(10)=6 we can rewrite the function as f(6).

f(6)= 6^2+1

f(6)=36+1

f(6)=37

Therefore ( f o g)(x) =f(g(10)) = 37.

Option 2:

"Write A New Equation"

In this option we will be writing out what f-compose-g of x is an equation and plugging 10 into our new expression.

For this we will be replacing all x's in f(x) with the function of g

So

( f o g)(x) = (x-4)^2+1

Now we solve for where x=10

( f o g)(10)= (10-4)^2+1

( f o g)(10)= (6)^2 +1

( f o g)(10)= 36+1

( f o g)(10)=37

Therefore ( f o g)(x) =f(g(10)) = 37.

In conclusion

( f o g)(x) =f(g(10)) = 37

Either method will get you to your answer, use whichever works best for you.

Answer 2

"f circle g" is an expression that means f(g(x)). If we want to know what f(2) is, we take the number 2 and plug it into f(x) to get f(2) so it would be (2)² + 1 = 4 + 1 = 5. We do the same thing when we are given f(g(x)) - we take g(x) and plug it into the function f wherever we find and "x". In this case, we have g(10). Well, what is g(10)? Well, it's 10 - 4 or 6, right? so we are being asked to find f(6).

f(6) = (6)² + 1 = 36 + 1 = 37

If we wanted to find and expression for f(g(x)) we could plug in g(x), which is "x - 4" into the function f(x) wherever we see an "x". So:

f(x) = x² + 1

f(g(x)) = (x - 4)² + 1 because g(x) is "x - 4"

So f(g(10)) = (10 - 4)² + 1

Answer 3

The open circle means to substitute the second function as the variable into the first function. The number in the parenthesis is the value used in the final function to find its value. I will replace the equation of g(x) in each position of the f(x) function.

f o g (x) = (x-4)² + 1 if x = 10 then x-4 = 6 ; 6² = 36. Then f o g (10) = 37.

Answer 4

(f circle g) is called f composed with g, and it basically means to evaluate g(x), and then plug that value into x in the f function. So, (f circle g)(10) = (f o g)(10) = f(g(10)).

Now, g(x) = x-4, so g(10) = 10-4 = 6. So now we plug in g(10), which is 6, into f(x).

So, assuming that the "x2" in the question is supposed to be x-squared, f(g(10)) = f(6) = 6²+1 = 37, so that will be your final answer.