Question

find the range of :
$f(x) = \frac{ {x}^{2} - x}{ {x}^{2} + 2x }$
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Answer 1

Step-by-step explanation:

Explanation:

The function can be rewritten as

f

(

x

)

=

x

2

+

2

x

+

1

+

1

=

(

x

+

1

)

2

+

1

. Notice that

(

x

+

1

)

2

≥

0

for all

x

∈

R

. Thus, the values

f

(

x

)

can be is all values greater than or equal to

1

.

Thus, the range is

{

y

∣

y

≥

1

}

or

y

∈

[

1

,

∞

[

.

Answer 2

Answer:

Overall, the steps for algebraically finding the range of a function are:

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).

Find the domain of g(y), and this will be the range of f(x).

If you can't seem to solve for x, then try graphing the function to find the range

YOYO

BRAINLIST AND TRY IT YOUR SELF WITH THIS 3-4 STEP PROCESS