What is the range of the function defined by f(x)=x+2/x

Question

What is the range of the function defined by f(x)=x+2/x :

a) [2,+∞)

b) (-∞,-2√2)∪(2√2,+∞)

c) (-∞,+∞)

d)( -∞,1)∪(1,+∞)

please explain how to find range

Answer 1

Greetings! Lets solve this shall we ?

In order to see what the range is, you must graph the function because it cannot be calculated algebraically. When we graph the function, we see it begins coming from negative infinity to -2√2 (-∞, -2√2) because of the lower hump of the graph has a tangent line of y = -2√2 and the top part of the graph has a tangent line at y = +2√2, where the graph continues from (2√2, ∞). The range consists of the set of all y-values where the function exists.

So altogether, the range is (-∞, -2√2] ∪ [2√2, ∞).

I hope this helped!

Answer 2

Finding the range of a function algebraically can be difficult, but not in this case.