Which functions domain consists of all real numbers except - 2?

a) f (x) = 1/x+2

b) f (x) = 2x

c) f (x) = 2x-2

d) f (x) = 1/vx+2

option (a) f (x) = 1/x+2

Step-by-step explanation:

(a) f (x) = 1 / x+2

To find the restriction for domain, we set the denominator = 0 and solve for x

x+2 = 0, so x=-2

When x=-2 then denominator becomes 0 that is undefined.

So, domain is all real numbers except - 2

(b) f (x) = 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

(c) f (x) = 2x-2

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f (x) = 1 / sqrt (x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than - 2