SOLUTION: Find the domain and range of the following function in interval form f(x)={{{ sqrt( x^2+3x-4 ) }}}*{{{ sqrt( 2-x-x^2 ) }}}

Algebra ->  Functions -> SOLUTION: Find the domain and range of the following function in interval form f(x)={{{ sqrt( x^2+3x-4 ) }}}*{{{ sqrt( 2-x-x^2 ) }}}      Log On


   

Question 1003153: Find the domain and range of the following function in interval form
f(x)=+sqrt%28+x%5E2%2B3x-4+%29+*+sqrt%28+2-x-x%5E2+%29+
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=sqrt%28+x%5E2%2B3x-4+%29+%2A+sqrt%28+2-x-x%5E2+%29+
domain:
all x excluding the value that makes ++x%5E2%2B3x-4+++ and ++2-x-x%5E2++equal to zero
++x%5E2%2B3x-4+=0++
++x%5E2-x%2B4x-4+=0++
++%28x%5E2-x%29%2B%284x-4%29+=0++
++x%28x-1%29%2B4%28x-1%29+=0++
++%28x%2B4%29%28x-1%29+=0++
=>x=1 or x=-4
+2-x-x%5E2+=0+
+2-2x%2Bx-x%5E2+=0+
+%282-2x%29%2B%28x-x%5E2%29+=0+
+2%281-x%29%2Bx%281-x%29+=0+
+%282%2Bx%29%281-x%29+=0+
=>x=1 or x=-2
so, domain is:
{ x element R : x+=+1 }
range:
{ y element R : y+=+0 }

here is better graph that shows you imaginary and real part:

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