$$\[ \mathrm{f}(x)=x^{2}+1 \quad \mathrm{~g}(x)=1-2 x \quad \mathrm{~h}(x)=\frac{1}{x}, x \neq 0 \quad \mathrm{j}(x)=5^{x} \]$$ Find $$$g(x) g(x)-\operatorname{gg}(x)$$$, giving your answer in the form $$$a x^{2}+b x+c$$$. .............................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_w20_qp_42 Year：2020 Question No：10(d)

Answer:

$4 x^{2}-8 x+2$ final answer

Knowledge points:

E2.2.3 Expand products of algebraic expressions. (e.g. expand (x + 4)(x – 7)) (Includes products of more than two brackets, e.g. (x + 4)(x – 7)(2x + 1))

E2.2.4.1 ax+bx+kay+kby

E2.9.1 Use function notation, e.g. f(x)=3x-5, f:x↦3x-5, to describe simple functions.

Solution:

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$$\[ \mathrm{f}(x)=x^{2}+1 \quad \mathrm{~g}(x)=1-2 x \quad \mathrm{~h}(x)=\frac{1}{x}, x \neq 0 \quad \mathrm{j}(x)=5^{x} \]$$ Find $$\(g(x) g(x)-\operatorname{gg}(x)\)$$, giving your answer in the form $$\(a x^{2}+b x+c\)$$. .............................................

Answer:

Knowledge points:

Solution:

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