Question 1102440
let . represent the composite function symbol.


Given f(x) = 3x^2 - x + 10 and g(x) = 1 - 20x, find g.f(x)


f(x) = 3x^2 - x + 10
g(x) = 1 - 20x


g.f(x) = g(f(x)) = g(3x^2 - x + 10)


since g(x) = 1 - 20x, replace x with (3x^2 - x + 10) to get:


g(f(x)) = 1 - 20 * (3x^2 - x + 10) = 1 - (60x^2 - 20x + 200) = 1 - 60x^2 + 20x - 200 = -60x^2 + 20x - 199


to confirm you did this correctly, do the following:


set x = 5 (randomly chosen, any valid number will do).


f(x) = 3x^2 - x + 10
f(5) = 3*5^2 - 5 + 10 = 80


you get f(x) = 80 when x = 5


now set x equal to f(x) to get x = 80


g(x) = 1 - 20x
g(80) = 1 - 20*80 = -1599


you get g(x) = -1599 when x = 80


now set x equal to 5 again.


g(f(x)) = -60x^2 + 20x - 199
g(5) = -60*5^2 + 20*5 - 199 = -1599


you get g(f(x) = -1599 when x = 5


you got f(x) = 80 when x = 5 and then got g(x) = -1599 when x = 80.


since this was the same answer as g(f(x)) = -1599 when x = 5, you just confirmed that the composite function was created successfully.


g.f(x) means find the value of f(x) first and then use that as the argument to g(x).