Given h(x) = 3x^2+2, hk(x) = x^2 -2, what is the function k?

Answer 1

Since the functions are multiplied, you divide

(x^2 - 2) / (3x^2 + 2)

1/3

_____________

3x^2 + 2 | x^2 - 2

x^2 + 2/3

-------------------

-2 and 2/3 = -8/3

So the quotient is 1/3 + -8/3 / (3x^2 + 2)

check [1/3 + (-8/3)/(3x^2 + 2 ) ] =

[(1/3)(3x^2 + 2) + (-8/3)]

--------------------------------- =

3x^2 + 2

(x^2 + 2/3 +- 8/3)

---------------------------------------- =

3x^2 + 2

(x^2 - 2)/(3x^2+2)

So k(x) = So the quotient is 1/3 + -8/3 / (3x^2 + 2)