In order to calculate (g o k)(0), first calculate (g o k)(x) = g[k(x)], as follow:
[tex]\begin{gathered} g(x)=5x^2+5x-4 \\ k(x)=5x^2+x-5 \\ (g\circ k)(x)=g\lbrack k(x)\rbrack=5\lbrack k(x)\rbrack^2+5\lbrack k(x)\rbrack-4 \\ (g\circ k)(x)=5\lbrack5x^2+x-5\rbrack^2+5\lbrack5x^2+x-5\rbrack-4 \end{gathered}[/tex]Next, replace the value x = 0 into the previous expression and simplify (this gives you the value of (g o k)(0) ):
[tex]\begin{gathered} (g\circ k)(0)=5\lbrack5(0)^2+0-5\rbrack^2+5\lbrack5(0)^2+0-5\rbrack-4 \\ (g\circ k)(0)=5\lbrack-5\rbrack^2+5\lbrack-5\rbrack-4 \\ (g\circ k)(0)=5\lbrack25\rbrack-25-4=125-25-4=96 \end{gathered}[/tex]Hence, the result is:
(g o k)(0) = 96
