Question
show all the steps it took to get your answer.
let f(x) = -2x+4 and g(x)=3x+1
a) Find f(x)*g(x)
b) find f (g(4))
let f(x) = -2x+4 and g(x)=3x+1
a) Find f(x)*g(x)
b) find f (g(4))
Answers
GPT 3.5
a) To find f(x)*g(x), we first need to find the product of f(x) and g(x).
f(x) = -2x + 4
g(x) = 3x + 1
f(x)*g(x) = (-2x + 4)*(3x + 1)
= -2x*3x - 2x*1 + 4*3x + 4*1
= -6x^2 - 2x + 12x + 4
= -6x^2 + 10x + 4
Therefore, f(x)*g(x) is -6x^2 + 10x + 4.
b) To find f(g(4)), we first need to find g(4) and then substitute it back into f(x).
g(x) = 3x + 1
g(4) = 3*4 + 1
= 12 + 1
= 13
Now we substitute g(4) back into f(x).
f(x) = -2x + 4
f(g(4)) = -2*13 + 4
= -26 + 4
= -22
Therefore, f(g(4)) is -22.
f(x) = -2x + 4
g(x) = 3x + 1
f(x)*g(x) = (-2x + 4)*(3x + 1)
= -2x*3x - 2x*1 + 4*3x + 4*1
= -6x^2 - 2x + 12x + 4
= -6x^2 + 10x + 4
Therefore, f(x)*g(x) is -6x^2 + 10x + 4.
b) To find f(g(4)), we first need to find g(4) and then substitute it back into f(x).
g(x) = 3x + 1
g(4) = 3*4 + 1
= 12 + 1
= 13
Now we substitute g(4) back into f(x).
f(x) = -2x + 4
f(g(4)) = -2*13 + 4
= -26 + 4
= -22
Therefore, f(g(4)) is -22.