How do you find the domain and range of t/sqrt(t^2-25) ?
1 Answer
Jan 22, 2018
Explanation:
f(t)=t/(sqrt(t^2-25))
"the denominator cannot equal zero as this would make"
"f(t) undefined"
rArrt^2-25!=0rArrt!=+-5
"also "t^2-25>0
rArr(t-5)(t+5)>0
rArrt<-5" or "t>5
rArr"domain is "(-oo,-5)uu(5,+oo)
f(t)=t/(sqrt(t^2(1-25/t^2)))=t/(tsqrt(1-25/t^2)
color(white)(f(t))=cancel(t)^1/(cancel(t)^1sqrt(1-25/t^2))
"as "t to+-oo,f(t)to1/sqrt(1-0)
rArry=-1,y=1larrcolor(blue)"excluded values"
rArr"range is "(-1,-oo)uu(1,+oo)
graph{x/(sqrt(x^2-25)) [-10, 10, -5, 5]}
