Question

find the domain and range of f(x)= root 4-x + 1/root x^2-1​

Answer 1

Answer:

Hope this may help you! Thanku

Answer 2

solution: the domain is  $(-$∞$,-1)U(1,4)$

• The domain function consists all the first elements of all ordered pairs, which is $x$, so let's find the value of $x$

• we know that,

                          $f(x)=\sqrt{4-x} +\frac{1}{\sqrt{x^{2} -1} }$

• for real value, it would be,

               $4-x\geq 0,x2-1 > 0$

               $4\geq x,x2 > 1\\x\leq 4, -1 > x > 1\\x\leq 4,x > 1 ,x < -1$

             ∴$x$∈$(-$∞$,-1)U(1,4)$

Therefore the domain is $(-$∞$,-1)U(1,4)$

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