If f (x) = x^2 + 5 and g (x) = 5x+4, what is[f o g (6)

You can do this a couple ways: either find g (6), then find f (x) of whatever that gives you (a 2-step process), or come up with a new expression to represent f (g (x)) and sub 6 into that (a 1-step process). I like the 1-step process more.

g (x) = 5x + 4; We want to sub this expression into every x in f (x) to get f (g (x)). If f (x) = x^2 + 5, then f (g (x)) = g (x) ^2 + 5 = (5x + 4) ^2 + 5. Now you can sub 6 into this equation and solve: f (g (6)) = (5 (6) + 4) ^2 + 5 = 1161.