2 questions. Function g(x) and a "set of values of x" issue.

2 questions. Function g(x) and a "set of values of x" issue.: "

Hi to all.



I've got 2 questions which are small but I just need to get somethings cleared in them.

Alright.



Q.1) The function g is defined by g:x ---> x-3(sqrt.x) for x>=0.

Solve the equation g(x)=10.



For this, I tried 2 things. First, I tried to square both sides in at attempt to make it a quadratic equation and factorize it. I got this:



10 = x-3(x^0.5)

(10)^2 = [x-3(x^0.5)]^2 (squaring both sides)

100=x^2 -3x -3x + 9x^0.25

0=x^2 -6x + 9x^0.25 -100



I'm stuck here. Don't know how to proceed. :(



Another thing I did was to multiply both sides by x:



10x = x^2-3(x^2)^1/2

10x = x^2 - 3x

x^2 = 10x+3x

x = 13x/x

x= 13



This, however, is not the correct answer.



So what do I have to do here? :confused:



Q.2) State the set of values of x for which x^3-3x^2-9x+27 is a decreasing function of x.

Given values of x are x=-1 and x=3.



I used (-inf,-1) and (3,+inf) to try get the values (inf=infinity).

I used -2 for -inf and 4 for +inf in the above equations but got positive values as answers, whereas the question says that it is a decreasing function of x.



How do I get the set of values of x?



Thanks for any help with these 2 questions. :)

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