Given:
The function are
[tex]f(x)=x^2-1[/tex]
[tex]g(x)=\sqrt{x}[/tex]
To find:
The value of [tex](f\circ g)(1)[/tex].
Solution:
We have,
[tex]f(x)=x^2-1[/tex]
[tex]g(x)=\sqrt{x}[/tex]
We need to find the value of [tex](f\circ g)(1)[/tex].
[tex](f\circ g)(1)=f(g(1))[/tex] [tex][\because (f\circ g)(x)=f(g(x))][/tex]
[tex](f\circ g)(1)=f(\sqrt{1})[/tex] [tex][\because g(x)=\sqrt{x}][/tex]
[tex](f\circ g)(1)=f(1)[/tex]
[tex](f\circ g)(1)=(1)^2-1[/tex] [tex][\because f(x)=x^2-1][/tex]
[tex](f\circ g)(1)=1-1[/tex]
[tex](f\circ g)(1)=0[/tex]
The value of [tex](f\circ g)(1)[/tex] is 0.
Therefore, the correct option is A.
