If #g(x)=x^2+5x+4# and #f(x)=x-2#, how do you find g(f(-2))?

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Answer 1 · 2016-11-14T23:07:36

#g(f(-2)) = 0#

This means to insert #f(x)# into #g(x)# and then evaluate when #x= -2#.

#g(f(x)) = (x- 2)^2 + 5(x - 2) + 4#

#g(f(x)) = x^2 - 4x + 4 + 5x -10 + 4#

#g(f(x)) = x^2 + x - 2#

#g(f(x)) = (x + 2)(x- 1)#

#g(f(-2)) = (-2 + 2)(-2 - 1)#

#g(f(-2)) = 0#

Hopefully this helps!