Chapter 2.1, Problem 8AYU

To determine

To fill:The restriction of $g\left(x\right)$ used to define the domain of the composite function $\frac{f}{g}$ .

Answer to Problem 8AYU

For composite function $\frac{f}{g}$ , in the domain, $g\left(x\right)\ne 0$ and should be the intersection of the domain of both f and g .

Explanation of Solution

Consider two sets A and B . If each element $x$ in the set A has exactly one element $y$ in the setB , the relation between them is known as a function. The ordered pair is $\left(x,y\right)$ .

The values of first coordinate $x$ is known as input values and the values of second coordinate $y$ is known as output values of a function.

Therefore, the set of input values represent the domain and set of output values represent the range of the function.

Hence, set of all images of the elements in the domain of a function is defined as the range of the function.

For a composite function $\frac{f}{g}$ , the domain of the function is defined by

  $\left(\text{Domain}\text{of}f\right)\cap \left(\text{Domain}\text{of}g\right)$

And the function $g\left(x\right)\ne 0$.