Question

If f(x) = 9x^(3/4) and g(x) = 3x^(1/8), what does (fg)(x) equal?

A) (fg)(x) = 27x^(11/8)
B) (fg)(x) = 27x^(7/8)
C) (fg)(x) = 12x^(11/8)
D) (fg)(x) = 12x^(7/8)

Answer 1

To find (fg)(x) with f(x) = 9x^(3/4) and g(x) = 3x^(1/8), we multiply the coefficients (9*3) and add the exponents (3/4 + 1/8). The result is (fg)(x) = 27x^(7/8).

Step-by-step explanation:

The question asks what (fg)(x) equals if f(x) = 9x3/4 and g(x) = 3x1/8. To find (fg)(x), we multiply f(x) by g(x), which is the same as multiplying their respective expressions. The product rule for exponents tells us that when multiplying two powers with the same base, we add the exponents. Applying this rule, we get:

1. Multiply the coefficients: 9 * 3 = 27.
2. Add the exponents with the same base (x): 3/4 + 1/8 = 6/8 + 1/8 = 7/8.

Therefore, (fg)(x) = 27x7/8. The correct answer is B) (fg)(x) = 27x7/8.