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Let f(x) = 4/x and g(x) = x + 4. Determine (f 0 g)(x) and its...

Let f(x) = 4/x and g(x) = x + 4. Determine (f 0 g)(x) and its domain.

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Answer #1

f(x) = 4 / x

g(x) = x + 4

(f o g)(x)

= f(g(x))

= f(x + 4)

= 4 / (x + 4)

Therefore,

(f o g)(x) = 4 / (x + 4)

Domain is the set of real values of x for which the function is real and defined.

In this case, for (f o g)(x) to be defined, the denominator must not be equal to 0

Therefore,

x + 4 0

=> x - 4

Therefore,

Domain is (- , - 4) U (- 4, )

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