Question

Identify where f is increasing and where f is decreasing.​ (Hint: Consider the graph

yequals=​f(x).)

f left parenthesis x right parenthesis equals StartRoot x minus 9 EndRootf(x)=x−9

Where is f​ increasing? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

f is increasing on the interval

nothing.

​(Type your answer in interval​ notation.)

B.

f is never increasing.

Where is f​ decreasing? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

f is decreasing on the interval

nothing.

​(Type your answer in interval​ notation.)

B.

f is never decreasing.

Answer 1

Let x and y be positive real numbers such that x<y.

Aiming for a contradiction, suppose √x>≥√y.

(1):

√x

≥

√y

(2)

√x

≥

√y

x

≥

y

Real Number Axioms: RO2RO2: compatibility with multiplication, (1)×(2)

Thus a contradiction is created.

Therefore:The square root function is always increasing.

Hence the given function is never decreasing.