Question

Let f(x)= 1/x-3 and g(x)= √x+5. What is the domain of (fog)(x)

Answer 1

Recall that :

`\text{ domain}((f\circ g)(x))=\text{ domain}(g(x))\cap\text{ domain}(f(g(x)))`

The function g is given by:

`g(x)=√(x+5)`

Hence:

`\text{ domain}(g(x))=[-5,\infty)`

Also,

`\text{ domain}(f(g(x))=\:[-5,\:4)\cup\left(4,\:\infty\:\right)`

Therefore, the required domain is:

[-5, 4) ∪ (4, ∞)

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