What is the range of the function f(x) = (x + 3)2 + 4?

Range of is [4,∞).

Step-by-step explanation:

Here we have , function  , We need to find range of this function . Let's find out:

In the function , Let's focus on : It's a perfect square whose value will be always positive and greater then equal to zero i.e.

⇒ , So minimum value of is 0 at x=-3 . ∴

⇒

⇒

⇒

Minimum value of is 4 , And maximum value of  can be ∞ as value of x can be increased . Therefore , Range of is [4,∞).

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

(3x-8) or (3x+8)

step-by-step explanation: