SOLUTION: I understand the function of a domain when f(x) is given along with the equation, but I do not understand how to find the domain of the function. f(x)=1-2x^2 f(x)=3^sqrt y-10

Question 68753This question is from textbook
: I understand the function of a domain when f(x) is given along with the equation, but I do not understand how to find the domain of the function.
f(x)=1-2x^2
f(x)=3^sqrt y-10
f(x)=4^sqrt x+1/x-2
Thank you for your help!!!!!
Christopher This question is from textbook

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I understand the function of a domain when f(x) is given along with the equation, but I do not understand how to find the domain of the function.
look for critical points of x ..like division by zero, square root of
negative number etc...which makes the operation in admissible. they
are to be eliminated from domain .hence domain is all real numbers except
those critical points.
f(x)=1-2x^2
there is no critical point. hence domain is all real values
f(x)=3^sqrt y-10
here sqrt(x-10) is involved.hence domain is all real values of x except
x<10
f(x)=4^sqrt x+1/x-2
same way (x+1)/(x+2)should be >=0....x=-1....or.....
both x+1 and x+2 should be +ve...hence x>-1
or
both x+1 and x+2 should be -ve....hence x<-2
hence domain is
x=-1,x>-1,x<-2
x=[-1,infinity)U(-infinity,-2)

Thank you for your help!!!!!
Christopher
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