How do you find h(x)=f(x)-g(x) given f(x)=6-x and g(x)=(x+1)^2-2?

1 Answer
Jun 28, 2017

h(x) = -x^2 - 3x + 7

Explanation:

Problems like these can be solved by simply substituting the equations for f(x) and g(x) into the h(x) equation:

f(x) = color(red)(6-x

g(x) = color(blue)((x+1)^2 - 2

h(x) = f(x) - g(x)

h(x) = color(red)(6-x) - (color(blue)((x+1)^2 - 2))

And a little simplifying..

h(x) = 6-x-(x^2 + 2x + 1 -2)

h(x) = 7 - 3x - x^2

or

color(green)(h(x) = -x^2 - 3x + 7