For the given functions f and g, find the following. For parts (a)–(d), also find the domain.

For the given functions and g, find the following. For parts (a)–(d), also find the domain.

(a) (f + g) (x)         (b) (f - g) (x)         (c) (f . g) (x)        (d)  (f / g) (x)

f (x) = x - 1;  g (x) = 2x2

Step 1:

The functions are and  .

(a)

Find the value of  .

All possible values of x is domain of the function.

The function is defined for all values of x .

The domain of is .

Step 2:

(b)

Find the value of .

All possible values of x is domain of the function.

The function is defined for all values of x .

The domain of is .

Solution:

(a) The domain of is .

(b) The domain of is .

Step 1:

The functions are and  .

(c)

Find the value of .

All possible values of x is domain of the function.

The function is defined for all values of x .

The domain of is .

Step 2:

(d)

Find the value of .

All possible values of x is domain of a function.

The denominator of a function should not be zero.

The domain of is .

Solution:

(c) The domain of is .

(d) The domain of is .