f left-parenthesis x right-parenthesis equals 3x superscript 3 baseline minus 4x superscript 2 baseline plus 6 x and g left-parenthesis x right-parenthesis equals 5x superscript 3 baseline plus 2x superscript 2 baseline minus 3x. What is f left-parenthesis x right-parenthesis minus g left-parenthesis x right-parenthesis?
To find f(x) - g(x), we will subtract the values of g(x) from f(x) term by term.
f(x) - g(x) = (3x^3 - 4x^2 + 6x) - (5x^3 + 2x^2 - 3x)
Simplifying, we combine like terms:
= 3x^3 - 4x^2 + 6x - 5x^3 - 2x^2 + 3x
= (3x^3 - 5x^3) + (-4x^2 - 2x^2) + (6x + 3x)
= -2x^3 - 6x^2 + 9x
Thus, f(x) - g(x) = -2x^3 - 6x^2 + 9x.