Suppose f(x)=7x-2 and g(x)= sqrt x^2-2x+9.
(f(g(x))=
(f(g(-2))=
To find f(g(x)), we need to substitute g(x) into the function f(x):
f(g(x)) = 7(g(x)) - 2
And to find f(g(-2)), we need to substitute g(-2) into the function f(x):
f(g(-2)) = 7(g(-2)) - 2
Now let's find g(x) and g(-2) separately:
1. g(x) = sqrt(x^2 - 2x + 9)
2. g(-2) = sqrt((-2)^2 - 2(-2) + 9)
= sqrt(4 + 4 + 9)
= sqrt(17)
Now let's substitute g(x) and g(-2) back into the function f(x) and f(-2), respectively:
1. f(g(x)) = 7(g(x)) - 2
= 7(sqrt(x^2 - 2x + 9)) - 2
2. f(g(-2)) = 7(g(-2)) - 2
= 7(sqrt(17)) - 2
Therefore, (f(g(x))) = 7(sqrt(x^2 - 2x + 9)) - 2 and (f(g(-2))) = 7(sqrt(17)) - 2.
To find the composition of two functions, f(g(x)), we need to substitute the value of g(x) into the function f.
1. Let's start with f(x) = 7x - 2.
2. Substitute g(x) into f(x): f(g(x)) = 7(g(x)) - 2.
3. Now, let's find g(x) = sqrt(x^2 - 2x + 9).
4. Substitute g(x) into the expression we found in step 2: f(g(x)) = 7(sqrt(x^2 - 2x + 9)) - 2.
For the second part of your question:
1. We need to evaluate f(g(-2)).
2. Let's find g(-2) first. Substitute x = -2 into g(x) = sqrt(x^2 - 2x + 9).
g(-2) = sqrt((-2)^2 - 2(-2) + 9) = sqrt(4 + 4 + 9) = sqrt(17).
3. Now, substitute the value of g(-2) into f(x) = 7x - 2: f(g(-2)) = 7(sqrt(17)) - 2.
So, the answers are:
- f(g(x)) = 7(sqrt(x^2 - 2x + 9)) - 2.
- f(g(-2)) = 7(sqrt(17)) - 2.
To find the value of f(g(x)), we need to substitute the expression for g(x) into f(x).
Given:
f(x) = 7x - 2
g(x) = √(x^2 - 2x + 9)
Let's substitute g(x) into f(x) to get f(g(x)):
f(g(x)) = 7(g(x)) - 2
Now, let's substitute g(x) in terms of x:
f(g(x)) = 7(√(x^2 - 2x + 9)) - 2
This is the expression for f(g(x)).
Now, let's find f(g(-2)):
To find f(g(-2)), we need to substitute -2 in place of x in the expression for g(x) and then substitute it into f(x).
Given:
g(x) = √(x^2 - 2x + 9)
Substitute -2 in place of x:
g(-2) = √((-2)^2 - 2(-2) + 9)
Simplifying the expression inside the square root:
g(-2) = √(4 + 4 + 9)
g(-2) = √(17)
Now, substitute g(-2) into f(x):
f(g(-2)) = 7(g(-2)) - 2
f(g(-2)) = 7(√(17)) - 2
This is the value of f(g(-2)).