Let \( f(x) =\frac {3x^2 + 5x + 8} {x^2 - x + 4 }\) and \(g(x) = x - 1. \) Find \(f(g(x)), \) evaluated when \( x = 1.\)
f(g(x) =
[ 3 (x - 1)^2 + 5(x - 1) + 8 ] / [ ( x - 1)^2 - (x - 1) + 4 ]
So
f(g(1) ) =
[ 3 (1 - 1)^2 + 5(1 - 1) + 8 ] / [ (1 - 1)^2 - (1 - 1) + 4 ] =
[ 3 (0)^2 + 5(0) + 8 ] / [ (0^2 - 0 + 4 ] =
] / [ 0 - 0 + 4 ] =
8 / 4 = 2
