( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60. The answers are option D and B
There are different type of Function
Different types of function demands different ways of solving them. Different types are simple function, function by substitution and function of function.
Given that
f(x) = [tex]x^{2}[/tex] + 9x - 14 and g(x) = [tex]x^{2}[/tex] - x + 3
( f - g )(x) will be the difference between f(x) and g(x)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - ( [tex]x^{2}[/tex] - x + 3)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - [tex]x^{2}[/tex] + x - 3
( f - g )(x) = 10x - 17
Also, if f(x) = [tex]3x^{2}[/tex] - 15 and g(x) = 1 - 2/3 x
( f ° g)(-6) means that we will evaluate g at -6, then evaluate f at the result of g(-6)
g(-6) = 1 - 2/3 (-6)
g(-6) = 1 + 4
g(-6) = 5
f(g(-6)) = 3([tex]5^{2}[/tex]) - 15
f(g(-6)) = 3 x 25 - 15
f(g(-6)) = 75 - 15
f(g(-6)) = 60
Therefore, ( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60
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