Question
Algebra Help Please!? multi choice(:?
1. Use the functions to answer the question.
f(x) = x2 + 3; g(x) = 6x
Which is equal to (f ? g)(x)?
6x2 + 3
6x3 + 18x
36x2 + 3
36x2 + 18
2. Use the functions to answer the question.
f(x) = 4x – 5; g(x) = x + 3
Which is equal to (g ? f)(x)?
4x – 2
4x + 7
4x + 12
5x – 2
3. Use the functions to answer the question.
f(x) = 2x + 1; g(x) = x2
Which is the value of (f ? g)(–5)?
-49
-19
51
11
5. Use the function to answer the question.
f(x) = 10 – x
What is the value of (f ? f)(3)?
1
3
7
8
Answers
1. f(x) = x2 + 3; g(x) = 6x
(f ? g)(x) = f(6x) = (6x)^2 + 3 (quite simply, replace x with 6x in the definition of f(x) )
= 36x^2 + 3
(choice number 3)
2. f(x) = 4x – 5; g(x) = x + 3
g(f(x)) = g(4x - 5) = (4x - 5) + 3 (again, replace x with 4x - 5 in the definition of g(x) )
= 4x - 2
(choice 1)
3. f(x) = 2x + 1; g(x) = x2
f(g(-5)) = f( (-5)^2) = f(25) (first simplify the value of g(x) at x = -5)
= 2*25 + 1 (put in x = 25 in f(x) )
= 51
(choice 3)
4. f(x) = 10 – x
f(f(3)) = f(10-3) = f(7) = 10 - 7 = 3
(choice 2)