High School

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Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .


What is (fg)(x) ?





x−4/x+3 where ​ x≠−3,4 ​


x−4/x+3 where x≠−3,3


x+4/x−3 where ​ x≠−3,3 ​


x+3/x−4 where x≠3,4

Let f x x2 9 and g x x2 7x 12 What is fg x x 4 x 3 where x 3 4 x 4

Answer :

[tex]f(x)=x^2-9 , g(x)=x^2-7x+12[/tex]

We need to find [tex]\frac{f}{g}(x)[/tex]

[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}[/tex]

We replace f(x) and g(x)

[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{x^2-9}{x^2-7x+12}[/tex]

Now factor the numerator and denominator and simplify it

[tex]\frac{x^2-9}{x^2-7x+12}[/tex]

[tex]\frac{(x+3)(x-3)}{(x-3)(x-4)}[/tex]

Cancel out x-3

[tex]\frac{(x+3)}{(x-4)}[/tex] where x not equal to 3,4

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Rewritten by : Barada

Final answer:

The product (fg)(x) of the functions f(x) = x² − 9 and g(x) = x² − 7x + 12 is found by multiplying the two functions together, resulting in (fg)(x) = x´ − 7x³ + 3x² + 63x − 108.

Explanation:

The question asks for the product (fg)(x) where f(x) = x2 − 9 and g(x) = x2 − 7x + 12. To find this product, we need to multiply f(x) and g(x) together:

(fg)(x) = f(x) × g(x)

Substitute the given functions:

(fg)(x) = (x2 − 9) × (x2 − 7x + 12)

Expand the product by using the distributive property (also known as FOIL for binomials):

(fg)(x) = x4 − 7x3 + 12x2 − 9x2 + 63x − 108

Combine like terms:

(fg)(x) = x4 − 7x3 + 3x2 + 63x − 108

This resulting expression is the product of f(x) and g(x), which is the function (fg)(x).