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if-f-x-3x-2-2-dx-and-f-2-9-then-f-2-




Question Number 146076 by Mrsof last updated on 10/Jul/21
if f(x)=∫(3x^2 −2)dx and f(2)=9 then  f(−2)= ?
$${if}\:{f}\left({x}\right)=\int\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}\right){dx}\:{and}\:{f}\left(\mathrm{2}\right)=\mathrm{9}\:{then} \\ $$$${f}\left(−\mathrm{2}\right)=\:? \\ $$
Answered by gsk2684 last updated on 10/Jul/21
f(x)=x^3 −2x+c  f(2)=9⇒8−4+c=9  ∴f(−2)=−8+4+5
$${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{2}{x}+{c} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{9}\Rightarrow\mathrm{8}−\mathrm{4}+{c}=\mathrm{9} \\ $$$$\therefore{f}\left(−\mathrm{2}\right)=−\mathrm{8}+\mathrm{4}+\mathrm{5} \\ $$

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