The function $\mathrm{f}$ is defined as follows. $$\mathrm{f}:x\mapsto 1+4x-x^2,\quad x

Question

The function $\mathrm{f}$ is defined as follows. $$\mathrm{f}:x\mapsto 1+4x-x^2,\quad x<a.$$ You are given that $\mathrm{f}^{-1}$ exists. By the method of completing the square, state the largest possible value of $a$.[2] For the rest of the question, take $a=0$. Find an expression for $\mathrm{f}^{-1}(x)$.[2] Find the exact solution of the equation $\mathrm{f}(x)=\mathrm{f}^{-1}(x)$.[2]

Accepted Answer

$a_{\max}=2$; $\mathrm{f}^{-1}(x)=2-\sqrt{5-x}$; $x=\dfrac{3-\sqrt{13}}2$

2025 RVHS Promo Q2

2025 RVHS Promo Q2

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