Question 1151339
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.


<a href = "https://www.mathsisfun.com/sets/functions-operations.html" target = "_blank">https://www.mathsisfun.com/sets/functions-operations.html</a>


<a href = "https://www.mathsisfun.com/sets/functions-composition.html" target = "_blank">https://www.mathsisfun.com/sets/functions-composition.html</a>


<a href = "https://www.purplemath.com/modules/fcnops.htm" target = "_blank">https://www.purplemath.com/modules/fcnops.htm</a>


<a href = "https://www.purplemath.com/modules/fcncomp2.htm" target = "_blank">https://www.purplemath.com/modules/fcncomp2.htm</a>