[tex]f(g(x))=x^2+4x+3[/tex]
Solution:
Given data:
[tex]f(x)=x^{2}-1[/tex]
[tex]g(x)=x+2[/tex]
To find f(g(x)):
Substitute g(x) into the function f(x).
[tex]f(g(x))=f(x+2)[/tex]
[tex]f(g(x))=(x+2)^2-1[/tex]
Apply algebraic rule:
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
[tex]f(g(x))=x^2+2\times 2x+2^2-1[/tex]
[tex]f(g(x))=x^2+4x+4-1[/tex]
[tex]f(g(x))=x^2+4x+3[/tex]
Therefore, [tex]f(g(x))=x^2+4x+3[/tex].
