Question

Let f(x) = x³+3, g(x)= x²-2, and h(x)= 2x+6. Find the rule for
the function fg/h

Answer 1

To find the rule for the function fg/h, multiply f(x) by g(x) to get fg(x) and then divide this by h(x). This results in the rule for fg/h(x) being (xµ - 2x³ + 3x² - 6)/(2x + 6).

Step-by-step explanation:

To find the rule for the function fg/h, we need to calculate the product of functions f(x) and g(x) and then divide it by function h(x). First, we'll find the product of f(x) and g(x):

• f(x) = x³ + 3
• g(x) = x² - 2

Multiplying these, we get:

fg(x) = f(x)g(x) = (x³ + 3)(x² - 2) = xµ - 2x³ + 3x² - 6

Now, we divide this product by h(x):

• h(x) = 2x + 6

So the function fg/h(x) is given by:

(fg/h)(x) = ü/(2x + 6)

fg/h(x) = (xµ - 2x³ + 3x² - 6)/(2x + 6)

That is the rule for the combined function fg/h.