SOLUTION: The domain of which function is -1 is less than or equal to x is less than or equal to 1? A. y=(3x+7)/(x^2-1) B. y=(x^2-1)/(3x+7) C. y=sqrt(1-x^2) D. y=1/sqrt(1-x^2)

Algebra ->  Trigonometry-basics -> SOLUTION: The domain of which function is -1 is less than or equal to x is less than or equal to 1? A. y=(3x+7)/(x^2-1) B. y=(x^2-1)/(3x+7) C. y=sqrt(1-x^2) D. y=1/sqrt(1-x^2)      Log On


   

Question 741544: The domain of which function is -1 is less than or equal to x is less than or equal to 1?
A. y=(3x+7)/(x^2-1)
B. y=(x^2-1)/(3x+7)
C. y=sqrt(1-x^2)
D. y=1/sqrt(1-x^2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
answer:
c. y=sqrt%281-x%5E2%29 because 1-x%5E2=0if 1=x%5E2 => 1=x or -1=x
domain: +-1+%3C=+x+%3C=1

if I draw vertical lines through x=-1 and x=1, you can see -1 and 1 lie on the blue line; so, -1 and 1 are part of solution


why the other one are not solution:
A. y=%283x%2B7%29%2F%28x%5E2-1%29

domain: all real numbers x except x=-1 and 1

B. y=%28x%5E2-1%29%2F%283x%2B7%29

if 3x%2B7=0 => 3x=-7 => x=-7%2F3



domain: all real numbers x except x=-1

D. y=1%2Fsqrt%281-x%5E2%29
denominator will be zero if 1-x%5E2=0, means if 1=x%5E2 => 1=x or -1=x
domain: +-1+%3C+x+%3C1


you can see -1 and 1 do not lie on the blue line; so, -1 and 1 are not a part of solution