Question

$f(x) = 4x + 3$
$g(x) = 5x - 4$
$fg(x) = 20x + p$


Find the value of
$p$


​

Answer 1

Let's see

$\\ \rm\rightarrowtail (fog)(x)=f(g(x))$

$\\ \rm\rightarrowtail f(5x-4)=20x+p$

$\\ \rm\rightarrowtail 4(5x-4)+3=20x+p$

$\\ \rm\rightarrowtail 20x-16+3=20x+p$

$\\ \rm\rightarrowtail -13=p$

Answer 2

Answer:

$\sf p = -13$

Step-by-step explanation:

Given functions:

$\sf f(x)=4x+3$

$\sf g(x)=5x-4$

$\sf fg(x)=20x+p$

$\sf fg(x)=f[g(x)]$

This means g(x) is substituted for x in f(x).

$\sf \implies f[g(x)]=4[g(x)]+3$

                 $\sf =4(5x-4)+3$

                  $\sf= 20x-16+3$

                  $\sf =20x-13$

$\sf f[g(x)]=f[g(x)]$

$\sf \implies 20x+p=20x-13$

$\sf \implies p=-13$