What is the domain and range of y =1/sqrt(17x+8)y=117x+8?

1 Answer
Jan 20, 2016

Domain: x in (-8/17,+oo)x(817,+)
Range: y in (0,+oo)y(0,+)

Explanation:

y=1/sqrt(h(x))y=1h(x)

  • Domain

The existence conditions are:

{(sqrt(h(x))!=0),(h(x)>=0):} => {(h(x)!=0),(h(x)>=0):} => h(x)>0

:.17x+8>0=>x> -8/17

:. Domain: x in (-8/17,+oo)

  • Range

we have to evaluate:

  • lim_(x rarr (-8/17)^+) f(x)=1/0^+=+oo

  • lim_(x rarr (+oo)) f(x)=1/(+oo)=0^+

     then #y=0# is a horizontal asymptote for #x rarr +oo#
    

:. Range: y in (0,+oo)