Respuesta :
Let's see
[tex]\\ \rm\rightarrowtail (fog)(x)=f(g(x))[/tex]
[tex]\\ \rm\rightarrowtail f(5x-4)=20x+p[/tex]
[tex]\\ \rm\rightarrowtail 4(5x-4)+3=20x+p[/tex]
[tex]\\ \rm\rightarrowtail 20x-16+3=20x+p[/tex]
[tex]\\ \rm\rightarrowtail -13=p[/tex]
Answer:
[tex]\sf p = -13[/tex]
Step-by-step explanation:
Given functions:
[tex]\sf f(x)=4x+3[/tex]
[tex]\sf g(x)=5x-4[/tex]
[tex]\sf fg(x)=20x+p[/tex]
[tex]\sf fg(x)=f[g(x)][/tex]
This means g(x) is substituted for x in f(x).
[tex]\sf \implies f[g(x)]=4[g(x)]+3[/tex]
[tex]\sf =4(5x-4)+3[/tex]
[tex]\sf= 20x-16+3[/tex]
[tex]\sf =20x-13[/tex]
[tex]\sf f[g(x)]=f[g(x)][/tex]
[tex]\sf \implies 20x+p=20x-13[/tex]
[tex]\sf \implies p=-13[/tex]