Given #f(x) = 4x + 5# and #g(x) = 7x - 2# how do you find (f - g)(7)?

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Answer 1 · 2017-09-25T20:26:43

See a solution process below:

First, let's find #(f - g)(x)#:

#(f - g)(x) = f(x) - g(x) = (4x + 5) - (7x - 2)#

#(f - g)(x) = 4x + 5 - 7x + 2#

#(f - g)(x) = 4x - 7x + 5 + 2#

#(f - g)(x) = (4 - 7)x + (5 + 2)#

#(f - g)(x) = -3x + 7#

To find #(f - g)(7)# substitute #color(red)(7)# for each occurrence of #color(red)(x)# in #(f - g)(x)#:

#(f - g)(color(red)(x)) = -3color(red)(x) + 7# becomes:

#(f - g)(color(red)(7)) = (-3 * color(red)(7)) + 7#

#(f - g)(color(red)(7)) = -21 + 7#

#(f - g)(color(red)(7)) = -14#