Question

Select the correct answer. If f(x)=x^1/2-x and g(x)=2x^3-x^1/2-x , find f(x) − g(x). A. -2x^3 - 2x - 2x^1/2 B. -2x^3 - 2x C. 2x^3 - 2x + 2x^1/2 D. -2x^3 + 2x^1/2

Answer 1

D. -2x^3 + 2x^1/2

Explanation:

Given

f(x) =x^1/2-x

g(x) = 2x^3-x^1/2-x

Required

f(x)-g(x)

f(x)-g(x) = x^1/2-x-(2x^3-x^1/2-x)

Open the parenthesis

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

Collect like terms

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

f(x)-g(x) = 2x^1/2+0-2x^3

f(x)-g(x) = -2x^3+2√x

Option D is correct