Question

Let f and g be functions.

The composition $\left(f\circ g\right)\left(x\right)$is defined for all values of x for which x is in domain of …. and g(x) is in the domain of ….

Short answer

The composition $\left(f\circ g\right)\left(x\right)$is defined for all values of x for which x is in domain ofg and g(x) is in the domain off.

Step-by-step solution

Step 1- Given Information

Given that, f and g are functions.

Step 2- Concept Used

The domain for the composition of $\left(f\circ g\right)\left(x\right)$is defined such that for all x in the domain of g such that g(x) is in the domain of f.

In other words, we can say that

$\left(f\circ g\right)\left(x\right)$is defined everywhere where g(x) and f(g(x)) are both defined.

Step 3- To find where the composition f∘gx is defined for all values of x.

By using Step 2, we can conclude that,

The composition $\left(f\circ g\right)\left(x\right)$ is defined for all values of x for which x is in domain of g and g(x) is in the domain off.