Edexcel – higher
(a) Find \(g(f(-3))\). (2 marks)
(b) Find \(g^{-1}(x)\). (2 marks)
\[\begin{aligned} &f(x)=(2x+3)^2,\quad g(x)=2x-1.\\ &f(-3)=(2(-3)+3)^2=(-6+3)^2=(-3)^2=9.\\ &g(f(-3))=g(9)=2\cdot 9-1=18-1=17. \end{aligned}\]
\[\begin{aligned} &y=2x-1\\ &y+1=2x\\ &x=\dfrac{y+1}{2}\\ &\therefore\; g^{-1}(x)=\dfrac{x+1}{2}. \end{aligned}\]
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