Question

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

Answer 1

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.