Question #de8d3

1 Answer
May 28, 2017

#-40x+31#

Explanation:

First, let's understand what #f(x)# means:

#f(x)# is a function that takes whatever is put inside the parentheses and does something to it. Some examples are:

#color(white)"XXX"f(color(red)3) = -4(color(red)3)+7#
#color(white)"X"f(color(blue)1200) = -4(color(blue)1200)+7#
#color(white)"XXX"f(color(brown)y) = -4(color(brown)y)+7#
#f(color(limegreen)(x^2-8)) = -4(color(limegreen)(x^2-8))+7#

So, to evaluate #f(color(orange)(g(x)))#, just plug #color(orange)(g(x))# into #f(x)#.

#f(color(orange)(g(x))) = -4(color(orange)(g(x)))+7#

#color(white)"XXX..-" = -4(color(orange)(10x-6))+7#

Now simplify.

#color(white)".-...." -4(10x-6)+7#

#= -40x-4(-6)+7#

#= -40x+24+7#

#= -40x+31#

Final Answer