Question

Consider the functions f(x) = x2 − 13 and g(x) = x + 5. What is the value of (f − g)(−4)? ...?

Answer 1

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f(x) = x2 - 13 
g(x) = x + 5

and are asked to compute "f-g" when x=-4. there are two ways of doing this. you can either first find f(-4) and g(-4) and then substract one from other like so:

f(−4)=(−4)2−13=16−13=3
g(−4)=−4+5=1

f(−4)−g(−4)=3−1=2

or you can create a new function that represents "f-g", call it "h", and work out h(-4) as follows:

h(x)=f(x)−g(x)=(x2−13)−(x+5)=x2−13−x−5=x2−x−18
h(−4)=(−4)2−(−4)−18=16+4−18=2