Function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto -{{x}^{2}}+4x+2,x2$. Show that&nbsp

Question

Function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto -{{x}^{2}}+4x+2,x>2$. Show that ${{\mathrm{f}}^{-1}}$ exists. Hence, find ${{\mathrm{f}}^{-1}}$, stating its domain and range.

Accepted Answer

${{\mathrm{f}}^{-1}}:x\mapsto 2+\sqrt{6-x}$; ${{D}_{{{\mathrm{f}}^{-1}}}}=(-\infty ,6)$ , ${{R}_{{{\mathrm{f}}^{-1}}}}=(2,\infty )$

Functions - One-to-One Functions and Inverse Existence

Functions - One-to-One Functions and Inverse Existence

Video Solution:

Solution:

Solution locked