given-that-the-composite-function-f-2-x-64x-45-find-f-x-

Question Number 91521 by jagoll last updated on 01/May/20

$${given}\:{that}\:{the}\: \\ $$$${composite} \\ $$$${function}\:{f}^{\mathrm{2}} \left({x}\right)\:=\:\mathrm{64}{x}+\mathrm{45}\: \\ $$$${find}\:{f}\left({x}\right)\: \\ $$

Commented by jagoll last updated on 01/May/20

$${yes}.\:{thank}\:{you} \\ $$

Commented by john santu last updated on 01/May/20

how to distinguish forms f^2 (x) with (f(x))^2 ?

$${how}\:{to}\:{distinguish}\:{forms} \\ $$$${f}^{\mathrm{2}} \left({x}\right)\:{with}\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \:?\: \\ $$

Commented by Prithwish Sen 1 last updated on 01/May/20

let f(x) = ax+b f{f(x)} = a^2 x+(ab+b) compairing a = ± 8,b= 5, −((45)/7) ∴ f(x)=8x+5 or −8x−((45)/7) please check.

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ax}+\mathrm{b} \\ $$$$\mathrm{f}\left\{\mathrm{f}\left(\mathrm{x}\right)\right\}\:=\:\mathrm{a}^{\mathrm{2}} \mathrm{x}+\left(\mathrm{ab}+\mathrm{b}\right) \\ $$$$\mathrm{compairing}\:\:\mathrm{a}\:=\:\pm\:\mathrm{8},\mathrm{b}=\:\mathrm{5},\:−\frac{\mathrm{45}}{\mathrm{7}} \\ $$$$\therefore\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}+\mathrm{5}\:\boldsymbol{\mathrm{or}}\:−\mathrm{8}\boldsymbol{\mathrm{x}}−\frac{\mathrm{45}}{\mathrm{7}}\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$

Commented by Prithwish Sen 1 last updated on 01/May/20

composite function of f = f○f = f{f(x)} which sometimes denote as f^2

$$\mathrm{composite}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\:=\:\mathrm{f}\circ\mathrm{f}\:=\:\mathrm{f}\left\{\mathrm{f}\left(\mathrm{x}\right)\right\} \\ $$$$\mathrm{which}\:\mathrm{sometimes}\:\mathrm{denote}\:\mathrm{as}\:\mathrm{f}^{\mathrm{2}} \\ $$

Commented by john santu last updated on 01/May/20

o..thank you. in my country if f^2 (x) = (f(x))^2 ⇒similar to sin^2 (x) = (sin (x))^2 if composite function f(f(x))

$${o}..{thank}\:{you}.\:{in}\:{my}\:{country} \\ $$$${if}\:{f}^{\mathrm{2}} \left({x}\right)\:=\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \:\Rightarrow{similar}\:{to} \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\:=\:\left(\mathrm{sin}\:\left({x}\right)\right)^{\mathrm{2}} \\ $$$${if}\:{composite}\:{function}\:{f}\left({f}\left({x}\right)\right) \\ $$

Commented by Prithwish Sen 1 last updated on 01/May/20