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

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Question 1102440: Given f(x)=3x^(2)-x+10 and g(x)=1-20x, find g.f(x)
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630) (Show Source):
You can put this solution on YOUR website!

Do the simplifying.

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Not sure how you mean the dot between g and f.
I setup an expression for composition of functions. If you wanted multiplication of functions then:

Do the multiplication and simplify.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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).