et lower f left parenthesis x right parenthesis equals x superscript 2 baseline plus 3 x minus 1 and lower g left parenthesis x right parenthesis equals x superscript 3 baseline plus 4 x superscript 2 baseline plus 1. Find left-parenthesis f minus g right-parenthesis left-parenthesis x right-parenthesis.
(1 point)
Responses
Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed minus 3 x squared plus 3 x
Image with alt text: Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed minus 3 x squared plus 3 x
Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals x cubed minus 3 x squared plus 3 x minus 2
Image with alt text: Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals x cubed minus 3 x squared plus 3 x minus 2
Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed minus 3 x squared plus 3 x minus 2
Image with alt text: Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed minus 3 x squared plus 3 x minus 2
Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed plus 7 x squared plus 3 x minus 2
The correct response is:
Left-parenthesis lower f minus lower g right-parenthesis left-parenthesis x right-parenthesis equals negative x cubed minus 3 x squared plus 3 x
To find f(x) - g(x), we need to subtract g(x) from f(x).
f(x) = x^2 + 3x - 1
g(x) = x^3 + 4x^2 + 1
Now we subtract g(x) from f(x):
f(x) - g(x) = (x^2 + 3x - 1) - (x^3 + 4x^2 + 1)
To simplify, let's combine like terms:
f(x) - g(x) = x^2 + 3x - 1 - x^3 - 4x^2 - 1
Now, let's rearrange the terms in descending order of exponents:
f(x) - g(x) = -x^3 - 4x^2 + x^2 + 3x - 1 - 1
Combining like terms once again, we get:
f(x) - g(x) = -x^3 - 3x^2 + 3x - 2
Therefore, f(x) - g(x) = -x^3 - 3x^2 + 3x - 2.