Function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto {{x}^{2}}+2x+3,x\le -1$. Show that&nbsp

Question

Function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto {{x}^{2}}+2x+3,x\le -1$. Show that ${{\mathrm{f}}^{-1}}$ exists. Hence, find ${{\mathrm{f}}^{-1}}$, stating its domain and range.

Accepted Answer

${{\mathrm{f}}^{-1}}:x\mapsto -1-\sqrt{x-2}$; ${{D}_{{{\mathrm{f}}^{-1}}}}=[2,\infty )$ , ${{R}_{{{\mathrm{f}}^{-1}}}}=(-\infty ,-1]$

Functions - One-to-One Functions and Inverse Existence

Functions - One-to-One Functions and Inverse Existence

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