SOLUTION: Let f(x) = 3x^2 and g(x)=3-x Evaluate: (A) (FG)(5) (B)(F/G)(5) (C)(FoG)(5)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Let f(x) = 3x^2 and g(x)=3-x Evaluate: (A) (FG)(5) (B)(F/G)(5) (C)(FoG)(5)      Log On


   

Question 1151339: Let f(x) = 3x^2 and g(x)=3-x Evaluate:
(A) (FG)(5)
(B)(F/G)(5)
(C)(FoG)(5)
Found 3 solutions by josgarithmetic, MathLover1, Theo:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Let F(x) = 3x^2 and G(x)=3-x Evaluate:

(A) (FG)(5)------------------- Multiplication of the functions and evaluate at x=5
(B)(F/G)(5)------------------ Divide function F by G and evaluate at x=5
(C)(FoG)(5)-------------- Use G as the input to F, and then evaluate at x=5.


C:
F%28G%28x%29%29=3%283-x%29%5E2
3%289-6x%2Bx%5E2%29
3x%5E2-18x%2B27
Now, let x equal to 5 and evaluate.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let f%28x%29+=+3x%5E2 and g%28x%29=3-x+
Evaluate:
(A)
%28FG%29%285%29
+%28FG%29%28x%29=3x%5E2%2A%283-x%29...plug in 5 for x
+%28FG%29%285%29=3%2A5%5E2%2A%283-5%29
+%28FG%29%285%29=3%2A25%2A%28-2%29
+%28FG%29%285%29=-150


(B)
%28F%2FG%29%285%29
+%28F%2FG%29%28x%29=3x%5E2%2F%283-x%29...plug in 5 for x
+%28F%2FG%29%285%29=%283%2A5%5E2%29%2F%283-5%29
+%28F%2FG%29%285%29=75%2F%28-2%29
+%28F%2FG%29%285%29=-37.5%29

(C)
%28FoG%29%285%29=F%28G%285%29%29
F%28G%28x%29%29=F%283-x%29=3%2A%283-x%29%5E2.....plug in 5 for x
F%28G%285%29%29=F%283-5%29=3%2A%28-2%29%5E2=3%2A4=12





Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 3x^2
g(x) = 3 - x

f(5) - 3 * 5^2 = 75
g(5) = 3 - 5 = -2

(f * g)(5) = 75 * -2 = -150 ***** 1

(f / g)(5) = 75 / -2 = -37.5 ***** 2

(f o g)(5) = f(-2) = 3 * (-2)^2 = 3 * 4 = 12 ***** 3

you can solve the function first and then replace x with 5 and you should get the same answer.

f(x) = 3x^2
g(x) = 3 - x

(f * g)(x) = f(x) * g(x) = 3x^2 * (3 - x) = 9x^2 - 3x^3.
when x = 5, this becomes 9 * 5^2 - 3 * 5^3 which becomes 9 * 25 - 3 * 125 which becomes 225 - 375 which becomes - 150 ***** 1

(f / g)(x) = f(x) / g(x) = 3x^2 / (3-x).
when x = 5, this becomes 3 * 5^2 / (3 - 5) which becomes 3 * 25 / -2 which becomes 75 / -2 which becomes -37.5 ***** 2

(f o g)(x) = f(f(x)) = f(3-x) = 3 * (3-x)^2 = 3 * (9 - 6x + x^2) = 27 - 18x + 3x^2.
when x = 5, this becomes 27 - 18 * 5 + 3 * 25 which becomes 27 - 90 + 75 which becomes 27 - 15 = 12 ***** 3

either way, you get the same answer.

here's some references you might find helpful.

https://www.mathsisfun.com/sets/functions-operations.html

https://www.mathsisfun.com/sets/functions-composition.html

https://www.purplemath.com/modules/fcnops.htm

https://www.purplemath.com/modules/fcncomp2.htm