SOLUTION: I NEED EXPLANATION IN A COUPLE OF MATH PROBLEMS they are all odd the answers are in the back of the book but i want to know how to do them can someone EXPLAIN HOW TO SOLVE THEM SO

Question 146648: I NEED EXPLANATION IN A COUPLE OF MATH PROBLEMS they are all odd the answers are in the back of the book but i want to know how to do them can someone EXPLAIN HOW TO SOLVE THEM SO I CAN BE READY FOR AN UPCOMING EXAM.i will greatly appreciated....
Directions: Use the function to evaluate the indicated expressions and simplify.
27) f(x)= x + 4 ; f(x^2), (f(x))^2
Directions: Find the domain of the function
37) f(x) = 2x
41) f(x) = (1)/(x-3)
43) f(x)= (x+2)/(x^2-1)
45) f(x)= f(x)= squareroot of (x-5)

Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
27) f(x)= x + 4 ; f(x^2), (f(x))^2
f(x^2)= x^2+4 (you have to put x^2 instead of x)
(f(x))^2 =(x+4)^2=x^2+8x+16
Directions: Find the domain of the function
The domain of polynomials are all real numbers
The domain of squareroot of f(x) are all real numbers that makes f(x)>=0
because the squareroot of a negative number is not real
The domain of quotient of polynomials (P(x)/Q(x)) are all real numbers that makes Q(x)not= to 0 because you can not divide by 0

37) f(x) = 2x domain are all real numbers (R)
41) f(x) = (1)/(x-3) domain are all real numbers except {x/x-3=0} so R-{3}
43) f(x)= (x+2)/(x^2-1) domain are all real numbers except
{x/x^2-1=0} so R-{1,-1}
45) f(x)= squareroot of (x-5)
domain are all real numbers that makes x-5>=0 so are real numbers x/x>=5
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