Question

If f(x)=(x+1)-1and g(x)=x-2 , what is the domain of f(x) ÷ g(x)?​

Answer 1

The domain of the f(x) ÷ g(x) is all real numbers except 2.

Explanation:

We have given two functions.

f(x) = (x+1)-1and g(x) = x-2

We have to find the domain of f(x)÷g(x).

f(x) ÷ g(x) = (x+1)-1 ÷ x-2

f(x) ÷ g(x) = x+1-1 ÷x-2

f(x) ÷ g(x) = x ÷ x-2

Hence, x-2 ≠ 0

x ≠ 2

The domain of the f(x) ÷ g(x) is all real numbers except 2.

Answer 2

The domain is all real numbers except x = 2

Explanation:

f(x) / g(x) = (x+1)-1 x

-------------- = --------------------

x-2 x-2

The domain is limited by the denominator. It cannot be zero

x-2 ≠ 0

Add 2 to each side

x-2+2 ≠ 0+2

x ≠2

X is all real numbers except 2