The function $\mathrm{f}$ is defined by $\mathrm{f}:x o \ln \left[ {{\left( x-1 ight)}^{2}}-k i

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x	o \ln \left[ {{\left( x-1 ight)}^{2}}-k ight]$, where $xdefine ${{\mathrm{f}}^{-1}}$, the inverse function of $\mathrm{f}$, in a similar form. show that the composite function ${{\mathrm{g}}^{-1}}{{\mathrm{f}}^{-1}}$ exists and find the range of this composite function.

Accepted Answer

max k = 9; f⁻¹(x) = 1 − √(eˣ + 8), x > 0; R_{g⁻¹f⁻¹} = (−π/2, tan⁻¹(−2))

2008 AJC P1 Q11

2008 AJC P1 Q11

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