QuestionGiven $f(x)=-3x+2$ and $g(x)=x^2+4x-7$ , find $f(x) \cdot g(x)$ .

Studdy Solution

STEP 1

Assumptions1. The functions are $f(x)=-3 x+$ and $g(x)=x^{}+4 x-7$ . We need to product of these two functions, i.e., $f(x) \cdot g(x)$

STEP 2

The product of two functions $f(x)$ and $g(x)$ is given by the formula $f(x) \cdot g(x) = f(x) \times g(x)$

STEP 3

Substitute the given functions into the formula.
$f(x) \cdot g(x) = (-3x +2) \times (x^{2}+ x-7)$

STEP 4

istribute the terms of the first function to each term of the second function.
$f(x) \cdot g(x) = -3x \cdot x^{2} -3x \cdot4x -3x \cdot -7 +2 \cdot x^{2} +2 \cdot4x +2 \cdot -7$

STEP 5

implify the multiplication in each term.
$f(x) \cdot g(x) = -3x^{3} -12x^{2} +21x +2x^{2} +8x -14$

STEP 6

Combine like terms.
$f(x) \cdot g(x) = -3x^{3} -10x^{2} +29x -14$ So, the product of the functions $f(x)=-3 x+2$ and $g(x)=x^{2}+4 x-$ is $f(x) \cdot g(x) = -3x^{3} -10x^{2} +29x -14$ .

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