Question

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

Answer 1

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.