The function $y=\mathrm{f}(x)$ is defined by $\mathrm{f}(x)=x^2-2x+6$, with $x\leq1$. Find \(\

Question

The function $y=\mathrm{f}(x)$ is defined by $\mathrm{f}(x)=x^2-2x+6$, with $x\leq1$. Find $\mathrm{f}^{-1}(x)$ and state its domain.[4] Find the range of the function $\mathrm{g}(x)=3+\sqrt{\mathrm{f}(x)}$.[2]

Accepted Answer

$\mathrm f^{-1}(x)=1-\sqrt{x-5}$, domain $[5,\infty)$; range of $\mathrm g$ is $[3+\sqrt5,\infty)$.

IB Math HL January 2016 P1 Q4

IB Math HL January 2016 P1 Q4

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