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

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Answer 1 · 2017-06-28T11:51:54

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

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#