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Question Number 155540 by cortano last updated on 02/Oct/21

  f(5−4x)=27x^(2000) −2187x^(204) −x^4 +3x+8  f(3x−7)=?

$$\:\:\mathrm{f}\left(\mathrm{5}−\mathrm{4x}\right)=\mathrm{27x}^{\mathrm{2000}} −\mathrm{2187x}^{\mathrm{204}} −\mathrm{x}^{\mathrm{4}} +\mathrm{3x}+\mathrm{8} \\ $$$$\mathrm{f}\left(\mathrm{3x}−\mathrm{7}\right)=? \\ $$

Answered by Rasheed.Sindhi last updated on 02/Oct/21

To transform 5−4x into 3x−7  replace x by ((−3x)/4)+3  f(5−4x)→f(5−4(((−3x)/4)+3))         =f(5−4(((−3x+12)/4))=f(3x−7)  =27(((−3x+12)/4))^(2000) −2187(((−3x+12)/4))^(204) −(((−3x+12)/4))^4 +3(((−3x+12)/4))+8

$$\mathcal{T}{o}\:{transform}\:\mathrm{5}−\mathrm{4}{x}\:{into}\:\mathrm{3}{x}−\mathrm{7} \\ $$$${replace}\:{x}\:{by}\:\frac{−\mathrm{3}{x}}{\mathrm{4}}+\mathrm{3} \\ $$$${f}\left(\mathrm{5}−\mathrm{4}{x}\right)\rightarrow{f}\left(\mathrm{5}−\mathrm{4}\left(\frac{−\mathrm{3}{x}}{\mathrm{4}}+\mathrm{3}\right)\right) \\ $$$$\:\:\:\:\:\:\:={f}\left(\mathrm{5}−\mathrm{4}\left(\frac{−\mathrm{3}{x}+\mathrm{12}}{\mathrm{4}}\right)={f}\left(\mathrm{3}{x}−\mathrm{7}\right)\right. \\ $$$$=\mathrm{27}\left(\frac{−\mathrm{3}{x}+\mathrm{12}}{\mathrm{4}}\right)^{\mathrm{2000}} −\mathrm{2187}\left(\frac{−\mathrm{3}{x}+\mathrm{12}}{\mathrm{4}}\right)^{\mathrm{204}} −\left(\frac{−\mathrm{3}{x}+\mathrm{12}}{\mathrm{4}}\right)^{\mathrm{4}} +\mathrm{3}\left(\frac{−\mathrm{3}{x}+\mathrm{12}}{\mathrm{4}}\right)+\mathrm{8} \\ $$

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