If #F(x) = 3x-2# and #G(x) = x^2+8#, what is #G(F(x))#?

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Answer 1 · 2017-07-01T13:12:56

See a solution process below:

To solve this problem we must substitute the #F(x)# function which is #color(red)(3x - 2)# for #color(red)(x)# in #G(x)#:

#G(color(red)(x)) = color(red)(x)^2 + 8# becomes:

#G(color(red)(F(x))) = color(red)((3x - 2))^2 + 8#

We can use this rule of the special form of quadratics to expand the squared term:

#(a - b)^2 = a^2 - 2ab + b^2#

Substituting:

#3x# for #a#

#2# for #b#

Gives:

#G(color(red)(F(x))) = (3x)^2 - (2 * 3x * 2) + 2^2 + 8#

#G(color(red)(F(x))) = 9x^2 - 12x + 4 + 8#

#G(color(red)(F(x))) = 9x^2 - 12x + 12#