24 Jun Domain: ##(-00 -1] uu [1 + oo)## Range: ##[0 + oo)## The dom
Domain: ##(-00 -1] uu [1 + oo)## Range: ##[0 + oo)## The domain of the function will be determined by the fact that the expression that’s under the radical must be positive for real numbers. Since ##x^2## will always be positive regardless of the sign of ##x## you need to find the values of ##x## that will make ##x^2## smaller than ##1## since those are the only values that will make the expression negative. So you need to have ##x^2 – 1 >=0## ##x^2 >=1## Take the square root of both sides to get ##|x| >= 1## This of course means that you have ##x >= 1 ## and ## x<=-1##The domain of the function will thus be ##(-00 -1] uu [1 + oo)##. The range of the function will be determined by the fact that the square root of a real number must always be positive. The smallest value the function can take will happen for ##x = -1## and for ##x=1## since those values of ##x## will make the radical term equal to zero. ##sqrt((-1)^2 -1) = 0 ## and ## sqrt((1)^2 -1 ) = 0##The range of the function will thus be ##[0 + oo)##.graph{sqrt(x^2-1) [-10 10 -5 5]}
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