provide-all-the-inverses-of-the-function-gx-x2-4x-7-and-identify-their-domains

Question

Provide all the inverses of the function ﻿g(x)=x2+4x+7g(x)=$$x^2+4x+7g(x)=x2+4x+7$$﻿ , and identify their domains.

Accepted Answer

﻿g−1(x)=−2+x−3﻿,domain:x≥$$3g^{-1}(x)=-2$$+\sqrt{x-3}﻿,domain:x\ge3g−1(x)=−2+x−3​﻿,domain:x≥3﻿﻿g−1(x)=−2−x−3﻿,domain:x≥$$3g^{-1}(x)=-2$$-\sqrt{x-3}﻿,domain:x\ge3g−1(x)=−2−x−3​﻿,domain:x≥3﻿

Answer

﻿g−1(x)=−2+x−7﻿,domain:x≥$$7g^{-1}(x)=-2$$+\sqrt{x-7}﻿,domain:x\ge7g−1(x)=−2+x−7​﻿,domain:x≥7﻿﻿g−1(x)=−2−x−7﻿,domain:x≥$$7g^{-1}(x)=-2$$-\sqrt{x-7}﻿,domain:x\ge7g−1(x)=−2−x−7​﻿,domain:x≥7﻿

Answer

﻿g−1(x)=−2+x−5﻿,domain:x≥$$5g^{-1}(x)=-2$$+\sqrt{x-5}﻿,domain:x\ge5g−1(x)=−2+x−5​﻿,domain:x≥5﻿﻿g−1(x)=−2−x−5﻿,domain:x≥$$5g^{-1}(x)=-2$$-\sqrt{x-5}﻿,domain:x\ge5g−1(x)=−2−x−5​﻿,domain:x≥5﻿

Answer

﻿g−1(x)=−2+x−1﻿,domain:x≥$$1g^{-1}(x)=-2$$+\sqrt{x-1}﻿,domain:x\ge1g−1(x)=−2+x−1​﻿,domain:x≥1﻿﻿g−1(x)=−2−x−1﻿,domain:x≥$$1g^{-1}(x)=-2$$-\sqrt{x-1}﻿,domain:x\ge1g−1(x)=−2−x−1​﻿,domain:x≥1﻿

Provide all the inverses of the function g(x)=x2+4x+7g(x)=x^2+4x+7g(x)=x2+4x+7 , and identify their domains.

Provide all the inverses of the function $g(x)=x^2+4x+7$ , and identify their domains.