The function $\mathrm{h}$ is defined by $\mathrm{h}:x\mapsto \frac{1}{2}{{x}^{2}}+3$, for $x\in \mat

Question

The function $\mathrm{h}$ is defined by $\mathrm{h}:x\mapsto \frac{1}{2}{{x}^{2}}+3$, for $x\in \mathbb{R}$. The function $\mathrm{g}$ is defined by $\mathrm{g}:x\mapsto \frac{x+1}{5x-1}$, for $x\in \mathbb{R}$, $x
e 0.2$. Find $\mathrm{gh}\left( 2 ight)$. [2] Find the value of $x$ for which $\mathrm{g}\left( x ight)=1.4$. [1] The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{x+a}{2x+b}$, for $x\in \mathbb{R}$, $x
e k$. Give an expression for $k$ and explain why this value of $x$ has to be excluded from the domain of $\operatorname{f}$. [2] The function $\mathrm{f}$ is such that $\mathrm{f}\left( x ight)={{\mathrm{f}}^{-1}}\left( x ight)$ for all $x$ in the domain of $\mathrm{f}$. Determine the possible values of $a$ and of $b$. [3] Find an expression for ${{\mathrm{f}}^{-1}}\left( -4 ight)$. [1]

Accepted Answer

$$\dfrac{4-a}{9}$$

N2021 P2 Q3

N2021 P2 Q3

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