Given the functions f(x) = x² - 2x and g(x) = 5 - x...?

Question

find (fg)(x)

Is it x³ - 7x² - 10x?

Answer 1

To solve this problem, we need to note the definition of (fg)(x).

(fg)(x) is defined to be f(x)g(x), which is, essentially, the product of two fractions. On a similar note, (f o g)(x) would mean something different, in case you meant that.

With that said, all you have to do is replace and expand.

f(x)g(x) = [x^2 - 2x][5 - x] = 5x^2 - x^3 - 10x + 2x^2
= 7x^2 - x^3 - 10x

If, however, you meant (f o g)(x), then this is defined to be f(g(x)).

f(g(x)) = f(5 - x)

At this point, you replace ALL occurrances of x in f(x) with 5-x.

f(5 - x) = [5 - x]^2 - 2[5 - x] = [25 - 10x + x^2] - 10 + 2x
= 15 - 8x + x^2

Answer 2

I think what you're being asked for is the compound function f(g(x)). There are several different notations for this and it tends to get confusing.

Just 'plug in' 5-x for every occurrance of x in f(x) to get
(5-x)² - 2(5-x) = 25 - 10x + x² - 10 + 2x = x² - 8x + 15

Hope that helps


Doug

Answer 3

I got -x^3 + 7x^2 - 10x = -x(x^2 - 7x + 10)

Answer 4

(fg)(x) = f(x)*g(x)
= (x^2 -2x)(5-x)
= 5x^2 - 10x - x^3 + 2x^2
= -x^3 + 7x^2 - 10x

Answer 5

is it f(g(x))
then (5-x)^2-2(5-x)
=25-10x+x^2-10+2x
=x^2-8x+15
if it is fog(x)
it is x^3-8x^2+15x
if it is f(x)*g(x)
-x^3+7x^2-10x

Answer 6

Is this composite functions?

(fg)(x)
(5-x)^2-2x
25-x^2-2x

Answer 7

Do you mean "find f(g(x))" ?

In that case, replace any "x" you find in f(x) with g(x) (replace then with 5-x) then solve.