1. To find (f∘g)(x), you first need to substitute g(x) into f(x). The composition (f∘g)(x) is written as f(g(x)).
2. g(x) = 1/x, so substitute 1/x into f(x)=x+4/2: f(g(x)) = (1/x) + 4/2.
3. Simplify the expression: f(g(x)) = 1/x + 2.
4. Therefore, the formula for (f∘g)(x) is 1/x + 2
- The domain of (f∘g)(x) is the set of all real numbers x for which the expression 1/x + 2 is defined.
- The function 1/x is not defined at x = 0 because division by zero is undefined.
- Therefore, the domain of (f∘g)(x) is all real numbers x except x = 0.
