Answer
$f(g[h(1)]) = 25$
Work Step by Step
$f(g[h(1)])$
$h(x) = x^{2} + x + 2$
$h(1) = (1)^{2} + 1 + 2$
$= 1 + 1 + 2$
$= 2 + 2$
$= 4$
$g(4) = 4(4) - 1$
$= 16 - 1$
$= 15$
$f(15) = 2(15) - 5$
$= 30 - 5$
$= 25$
$f(g[h(1)]) = 25$