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

`\sf p = -13`

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`