# What is the continuity of the composite function #f(g(x))# given #f(x)=1/sqrtx# and #g(x)=x-1#?

##### 1 Answer

Feb 24, 2017

The domain is

#### Explanation:

The process here is to verify first the domain of

This is a linear function, so is defined on all values of

There will be two types of restriction on the domain in this problem.

•When the number underneath the

#√# is less than#0# .

•When the denominator equals#0# .

The number under the square root will be negative whenever

In other words, the composition is continuous for all values of

Hopefully this helps!