$$\[ \mathrm{f}(x)=4 x-1 \quad \mathrm{~g}(x)=x^{2} \quad \mathrm{~h}(x)=3^{-x} \]$$ Show that $$\(\mathrm{g}(3 x-2)-\mathrm{h}(-3)\)$$ can be written as $$\(9 x^{2}-12 x-23\)$$.
Exam No：0580_m20_qp_42 Year：2020 Question No：10(d)(i)
Answer:
\((3 x-2)^{2}-3^{-(-3)}\)
\(9 x^{2}-6 x-6 x+4-27\) or
\(9 x^{2}-12 x+4-27\)
leading to \(9 x^{2}-12 x-23\)
\(9 x^{2}-6 x-6 x+4-27\) or
\(9 x^{2}-12 x+4-27\)
leading to \(9 x^{2}-12 x-23\)
Knowledge points:
E2.9.1 Use function notation, e.g. f(x)=3x-5, f:x↦3x-5, to describe simple functions.
E2.9.2 Find inverse functions
E2.9.3 Form composite functions as defined by gf(x)=g(f(x)).
Solution:
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