Answer:
[tex]x^2-2[/tex]
Step-by-step explanation:
[tex](g \circ f)(x)[/tex]
[tex]g(f(x))[/tex]
Replace [tex]f(x)[/tex] with [tex]x^2-3[/tex] since we are given [tex]f(x)=x^2-3[/tex]:
[tex]g(x^2-3)[/tex]
Replace [tex]x[/tex] in [tex]x+1[/tex] with [tex]x^2-3[/tex] since [tex]g(x)=x+1[/tex]:
[tex](x^2-3)+1[/tex]
Group like terms together:
[tex]x^2+(-3+1)[/tex]
Simplify:
[tex]x^2+(-2)[/tex]
[tex]x^2+-2[/tex]
[tex]x^2-2[/tex]
