- Given the functions \(f(x)=x-2\) and \(g(x)=x^2\), determine the equation of \(f(g(x))\) and sketch its graph showing all intercepts. (2 marks)
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- Evaluate \(g(f(-1))\). (1 mark)
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Show Answers Only
a.
b. \(g(f(-1))=9\)
Show Worked Solution
a. \(f(x)=x-2, \ g(x)=x^2\)
\(f(g(x))=x^2-2\)
\(\text{Intercepts:} \ \ x^2-2=0 \ \Rightarrow \ x= \pm \sqrt{2}\)
b. \(f(-1)=-1-2=-3\)
\(g(f(-1))=g(-3)=9\)