If g(x) = 2x-3 and h(x) = x^2 + 7x + 10, find hog(x).

Answer 1

This is a composition of functions.

hog(x) = h(g(x))

In other words, the x value for h(x) will be g(x).

So,

hog(x) = h(g(x)) = (2x-3)²+7(2x-3)+10

= (4x²-6x-6x+9) +(14x-21)+10

= 4x²-12x+9+14x-21+10

= 4x²+2x-2

hog(x)=4x²+2x-2