Determine the formula and domain for (f 0 g)(x) when f(x)=(x-3) and g(x)=x^2-4

f(x) = (x - 3)

g(x) = x^2 - 4

(fog)(x) = f(g(x)) = f(x^2-4) = x^2 - 4 - 3 = x^2 - 7

For every value of x (fog)(x) exists.

So domain = all real numbers

This is the plot of x^2 - 7

ANSWER:

(fog)(x) = x^2 - 7

Domain = all real numbers

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