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 answer is E. I think

Answer 2

Answer:

The correct option is C.

Step-by-step explanation:

The given functions are

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

$g(x)=x^{\frac{1}{2}}$

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

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

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

According to the property of exponent,

$\frac{x^a}{x^b}=x^{a-b}$

Using this property we get

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

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

Therefore the correct option is C.