Question

Let f(x) = x + 1 and g(x)=1/x. The graph of (f*g)(x) is shown below. What is the range of (f*g) (x)

A.all real numbers except y=-1
B.all real numbers except y=0
C.all real numbers except y=1
D.all real numbers

Answer 1

C.

Explanation:

All real numbers except y=1

Answer 2

For this case we have the following functions:

`f (x) = x + 1\\g (x) = \frac {1} {x}`

By definition we have to:

`(f * g) (x) = f (x) * g (x)`

So:

`f (x) * g (x) = x + 1 * \frac {1} {x} = \frac {x + 1} {x}`

The domain of the function is given by the values for which the function is defined. The function is not defined for x = 0.

Then, the domain is given by all real numbers except 0.

The range is the set of all values of and valid.

Then the range is given by all reals except 1.

Answer:

Option C