ANSWER
[tex]g(f( - 1)) = \frac{1}{5 }[/tex]
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} [/tex]
and
[tex]g(x) = \frac{1}{2x + 3} [/tex]
[tex]g(f(x)) = g( {x}^{2} )[/tex]
[tex]g(f(x)) = \frac{1}{2{x}^{2} + 3 } [/tex]
To find g(f(-1)), we substitute x=-1, to obtain;
[tex]g(f( - 1)) = \frac{1}{2{( - 1)}^{2} + 3 } [/tex]
We simplify the square in the denominator to get,
[tex]g(f( - 1)) = \frac{1}{2+ 3 } [/tex]
We now add the denominator to obtain;
[tex]g(f( - 1)) = \frac{1}{5 } [/tex]
