Given:
[tex]f(x)=3x-7\text{ and }g(x)=\frac{x+1}{x-1}.[/tex]
Required:
We need to find the value of f(g(3)).
Explanation:
Substitute x =3 in the equation g(x) to find g(3).
[tex]g(3)=\frac{3+1}{3-1}.[/tex]
[tex]g(3)=\frac{4}{2}.[/tex][tex]g(3)=2.[/tex]
Substitute g(3)=2 in f(g(3)).
[tex]f(g(3))=f(2)[/tex]
Substitute x=2 in the equation f(x).
[tex]f(2)=3(2)-7[/tex]
[tex]f(2)=6-7[/tex][tex]f(2)=-1[/tex]
[tex]Substitute\text{ f\lparen2\rparen=-1 in }f(g(3))=f(2).[/tex]
[tex]\text{ }f(g(3))=-1.[/tex]
Final answer:
[tex]\text{ }f(g(3))=-1.[/tex]
