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

Question

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

 

Answer 1

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 .

Answer 2

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 .