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Q5.

Expert-verifiedFound in: Page 216

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Let f and g be functions.**

**The function (f + g) (x) is defined for all values of x that are in the domains of both …. and ….****The function (fg) (x) is defined for all values of x that are in the domains of both …. and ….****The function (f/g) (x) is defined for all values of x that are in the domains of both …. and …., and g(x) is not equal to ….**

- The function (f + g) (x) is defined for all values of x that are in the domains of both f and g.
The function (fg) (x) is defined for all values of x that are in the domains of both f and g.

The function (f/g) (x) is defined for all values of x that are in the domains of both f and g and g(x) is not equal to 0.

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

The function (f + g) (x) is defined as

$\left(f+g\right)\left(x\right)\text{=}f\left(x\right)\text{}+\text{}g\left(x\right)$

The domain of f + g is the intersection of the domains i.e.,$X\cap Y$

Therefore, we get

The function (f + g) (x) is defined for all values of x that are in the domains of both f and g.

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

The function (f/g) (x) is defined as

The domain of fg is the intersection of the domains i.e.,

Therefore, we get

The function (fg) (x) is defined for all values of x that are in the domains of both f and g.

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

The function (f/g) (x) is defined as

The domain of f/g is the intersection of the domains i.e., and

Therefore, we get

The function (f/g) (x) is defined for all

values of x that are in the domains of both f and g and g(x) is not equal to 0.

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