Answer:
[tex](f.g)x = {x}^{2} + 24x + 140[/tex]
Step-by-step explanation:
[tex]given \\ f(x) = x ^{2} + 10x + 21 \: and \: g(x) = x + 7[/tex]
[tex]as \: we \: know \: (f.g)x \: is \: same \: as[/tex]
[tex]f(g(x))[/tex]
[tex]so \: [/tex]
[tex]f(x + 7) = ( x + 7) ^{2} + 10(x + 7) + 21[/tex]
[tex]f(x + 7) = {x}^{2} + 14x + 49 + 10x + 70 + 21[/tex]
[tex]f(x + 7) = x^{2} + 24x + 140[/tex]
[tex]therefore [/tex]
[tex](f.g)x = {x}^{2} + 24x + 140[/tex]
