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Question Number 169319 by otchereabdullai@gmail.com last updated on 28/Apr/22

if f(2x−1)=x^2 −3x+2, find f(2)

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{2x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2},\:\:\mathrm{find}\:\mathrm{f}\left(\mathrm{2}\right) \\ $$

Commented by infinityaction last updated on 28/Apr/22

x→((x+1)/2) f(x) = (((x+1)/2))^(2 ) −3(((x+1)/2))+2 f(2) = (9/4) −(9/2)+2 f(2) = −(1/4)

$${x}\rightarrow\frac{{x}+\mathrm{1}}{\mathrm{2}} \\ $$$${f}\left({x}\right)\:=\:\left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}\:} −\mathrm{3}\left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)+\mathrm{2} \\ $$$${f}\left(\mathrm{2}\right)\:=\:\frac{\mathrm{9}}{\mathrm{4}}\:−\frac{\mathrm{9}}{\mathrm{2}}+\mathrm{2} \\ $$$${f}\left(\mathrm{2}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Commented by otchereabdullai@gmail.com last updated on 28/Apr/22

Thank you

$$\mathrm{Thank}\:\mathrm{you} \\ $$

Answered by alephzero last updated on 28/Apr/22

f(2x−1) = x^2 −3x+2 2 = 2x−1 ⇒ x = 1.5 ⇒ f(2(1.5)−1) = 1.5^2 −3(1.5)+2 = 2.25−4.5+2 = −0.25

$${f}\left(\mathrm{2}{x}−\mathrm{1}\right)\:=\:{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2} \\ $$$$\mathrm{2}\:=\:\mathrm{2}{x}−\mathrm{1} \\ $$$$\Rightarrow\:{x}\:=\:\mathrm{1}.\mathrm{5} \\ $$$$\Rightarrow\:{f}\left(\mathrm{2}\left(\mathrm{1}.\mathrm{5}\right)−\mathrm{1}\right)\:=\:\mathrm{1}.\mathrm{5}^{\mathrm{2}} −\mathrm{3}\left(\mathrm{1}.\mathrm{5}\right)+\mathrm{2} \\ $$$$=\:\mathrm{2}.\mathrm{25}−\mathrm{4}.\mathrm{5}+\mathrm{2}\:=\:−\mathrm{0}.\mathrm{25} \\ $$

Commented by otchereabdullai@gmail.com last updated on 28/Apr/22

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

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