Mathematics

Mathematics

Problem

Consider the quadratic function q(x)=x2+4x+1q(x)=x^{2}+4x+1. Exactly one of the following pairs (domain,q−1(y))(\text{domain},q^{-1}(y)) correctly gives a domain on which qq is one–to–one together with the corresponding inverse. Identify it. a) [−2,∞),  q−1(y)=−2−y+3[-2,\infty),\; q^{-1}(y)=-2-\sqrt{y+3} b) (−∞,−2],  q−1(y)=−2+y+3(-\infty,-2],\; q^{-1}(y)=-2+\sqrt{y+3} c) [−2,∞),  q−1(y)=−2+y+3[-2,\infty),\; q^{-1}(y)=-2+\sqrt{y+3} d) [2,∞),  q−1(y)=−2+y+3[2,\infty),\; q^{-1}(y)=-2+\sqrt{y+3}

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