PLEASE HELP 20 POINTS!!!! f(x)=x^3+6x^2+x^1/2 and g(x)=x^1/2 Find f(x)/g(x) A).x&5/2+6x&3/2-1 B).(x^5+6x^3+1)^1/2 C).x^5/2+6x^3/2+1 D).x^3/2+6x+x^1/4 E).x^3/2-6x+x^1/4

Question

asked Sep 24, 2018 164k views

1 Answer

Jemlifathi · Answer 1 · 2018-09-27T12:27:41+0000

Answer:

The correct option is C.

Explanation:

The given functions are

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

$g(x)=x^{(1)/(2)}$

We have to find the value of f(x)/g(x).

$(f(x))/(g(x))=\frac{x^3+6x^2+x^{(1)/(2)}}{x^{(1)/(2)}}$

$(f(x))/(g(x))=\frac{x^3}{x^{(1)/(2)}}+\frac{6x^2}{x^{(1)/(2)}}+\frac{x^{(1)/(2)}}{x^{(1)/(2)}}$

According to the property of exponent,

(x^a)/(x^b)=x^(a-b)

Using this property we get

$(f(x))/(g(x))=x^{3-(1)/(2)}+6x^{2-(1)/(2)}+1$

$(f(x))/(g(x))=x^{(5)/(2)}+6x^{(3)/(2)}+1$

Therefore the correct option is C.