fx x3 6x2 x12 and gx x12 Find fxgx x52 6x32 1 x5 6x3

f(x) = x^3 + 6x^2 + x^1/2 and g(x) = x^1/2. Find f(x)/g(x). x^5/2 + 6x^3/2 - 1 (x^5 + 6x^3 + 1)^1/2 x^5/2 + 6x^3/2 + 1 x^3/2 + 6x + x^1/4 x^3/2 - 6x + x^1/4

Solution

f(x) = x^3 + 6x^2 + x^1/2

g(x) = x^1/2

f(x) / g(x) : Divide the two functions:

f(x)/ g(x) = (  x^3 + 6x^2 + x^1/2)/ (x^1/2)

Use property : x^a/x^b = x^(a-b)

= x^(3-1/2) +6x^(2-1/2) +x^(1/2 -1/2)

= x^5/2 + 6x^3/2 +1

Option B