f(x) = xsquared + 2x + 5 and g(x) = x-1 then f(g)(x)

Question

f(x) =

 

Answer 1

You gave

f(x) = x² + 2x + 5

g(x) = x - 1

To get f(g(x)) you just need to replace every x with g(x) in the formula for f(x) and then simplify.

In this case you would get

f(g(x)) = g(x)² + 2g(x) + 5

            = (x - 1)² + 2(x - 1) + 5

            = x² - 2x + 1 + 2x - 2 + 5

            = x² + 4