Find (f composed with g)(x) and (g composed with f)(x)?

The language of the question is the hardest part. By substituting x = 2 we find f(x) = 11 and your answer is correct.

(g composed with f)(x) is the last line of the question, namely =2 .

Composed With

The function (f composed with g)(x) is read "f of g of x," so for g(x) = 2 it would be:

f(g(x)) = 2(g(x)^3) - 3(g(x)^2) + 4g(x) - 1

= f(2)

= 2(2^3) - 3(2^2) + 4(2) - 1

= 11

Since g(x) = 2 for all x, and f(x) gets plugged into g(x) when you find (g composed with f)(x), g(f(x)) will always be 2 no matter what f(x) turns out to be. The answer is "all real numbers" because setting x equal to any real number will give you the same result.

You're right about 11, and g composed with f I'm pretty sure would be 2, since there are no variables in g(x).

(f composite g)=(f o g)(x), to get the value of it, you will substitute the value of g(x) to all x in f(x),

therefore,

(f o g)(x)=

2(2)^3-3(2)^2+4(2)-1

2(8)-3(4)+8-1

16-12+8-1

(f o g) = 15

since there is no x in g(x), there is no solution for (g o f)(x).

f(x) is the outside function, so start with 4x - 2 g(x) gets inserted into f(x) as 4(x^2) - 2 h(x) gets inserted into f(g(x)) as 4(6 - x)^2 - 2 Now solve: 4(6 - x)^2 - 2 4(x^2 - 12x + 36) - 2 4x^2 - 48x + 144 - 2 4x^2 - 48x + 142 If you wanted to simplify it further you could finish with: 2(2x^2 - 24x + 71)