Suppose f(x)=6x+4 and g(x)= sqrt x^2+3x+6

(f(g(x))=
(f(g(x)(-5)=

To find the composition of f(g(x)), we substitute g(x) in place of x in the function f(x):

f(g(x)) = 6 * (g(x)) + 4

Now let's find g(x):

g(x) = √(x^2 + 3x + 6)

Substituting g(x) back into f(x):

f(g(x)) = 6 * (√(x^2 + 3x + 6)) + 4

To find f(g(x)(-5)), we substitute -5 in place of x in the function f(g(x)):

f(g(x)(-5)) = 6 * (√((-5)^2 + 3(-5) + 6)) + 4

Simplifying further:

f(g(x)(-5)) = 6 * (√(25 - 15 + 6)) + 4
= 6 * (√(16)) + 4
= 6 * 4 + 4
= 24 + 4
= 28

Therefore, f(g(x)(-5)) is equal to 28.

To find the composite function f(g(x)), we need to substitute g(x) into f(x) and simplify.

Given: f(x) = 6x + 4 and g(x) = √(x^2 + 3x + 6)

1. Substitute g(x) into f(x):
f(g(x)) = 6(g(x)) + 4

2. Substitute g(x) with its expression:
f(g(x)) = 6(√(x^2 + 3x + 6)) + 4

To find the value of f(g(x)) when x = -5, substitute -5 into the expression for x:

f(g(-5)) = 6(√((-5)^2 + 3(-5) + 6)) + 4

Simplifying the expression inside the square root:
f(g(-5)) = 6(√(25 - 15 + 6)) + 4
f(g(-5)) = 6(√(16)) + 4
f(g(-5)) = 6(4) + 4

Now, solve the expression:

f(g(-5)) = 24 + 4
f(g(-5)) = 28

Therefore, f(g(x)) = 6x + 4 when x = -5 is equal to 28.

To find the value of f(g(x)), we need to substitute the expression for g(x) into f(x) and simplify.

Given: f(x) = 6x + 4
g(x) = sqrt(x^2 + 3x + 6)

Substituting g(x) into f(x), we get:

f(g(x)) = 6(sqrt(x^2 + 3x + 6)) + 4

Now, let's find f(g(x)) for the specific value of x = -5:

f(g(-5)) = 6(sqrt((-5)^2 + 3(-5) + 6)) + 4

First, simplify the expression inside the square root:

(-5)^2 = 25
3(-5) = -15

Now, substitute these values into the expression:

sqrt(25 - 15 + 6) = sqrt(16) = 4

Now, we have:

f(g(-5)) = 6(4) + 4

Simplifying further:

6(4) + 4 = 24 + 4 = 28

Therefore, f(g(-5)) = 28.