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

given that the   composite  function f^2 (x) = 64x+45   find f(x)

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

Commented by jagoll last updated on 01/May/20

yes. thank you

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

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

where are you from Sir ?

$$\mathrm{where}\:\mathrm{are}\:\mathrm{you}\:\mathrm{from}\:\mathrm{Sir}\:? \\ $$

Commented by Joel578 last updated on 01/May/20

indonesia?

$${indonesia}? \\ $$

Commented by mathmax by abdo last updated on 01/May/20

f(f) is noted fof  and  f^2 =f×f

$${f}\left({f}\right)\:{is}\:{noted}\:{fof}\:\:{and}\:\:{f}^{\mathrm{2}} ={f}×{f} \\ $$

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