Let f(x) = x + 8 and #g(x) = x^2 - 6x - 7# how do you find f(g(2))?

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Answer 1 · 2017-03-31T11:53:27

See the entire solution process below:

First, evaluate #g(2)# by substituting #color(red)(2)# for each occurrence of #color(red)(x)# in the function #g(x)#:

#g(color(red)(x)) = color(red)(x)^2 - 6color(red)(x) - 7# becomes:

#g(color(red)(2)) = color(red)(2)^2 - (6 xx color(red)(2)) - 7#

#g(color(red)(2)) = 4 - 12 - 7#

#g(color(red)(2)) = -15#

We can now substitute #color(blue)(g(2))# which is #color(blue)(-15)# for each occurrence of #color(blue)(x)# in the function #f(x)#:

#f(color(blue)(x)) = color(blue)(x) + 8# becomes:

#f(color(blue)(-15)) = color(blue)(-15) + 8#

#f(color(blue)(-15)) = -7#

Therefore, #f(g(2)) = -7#