Consider the function f(x)=3x+4x−2,x≠2 Find a function on a suitable domain such that goƒ(x) = x = ƒog(x)

To find a function on a suitable domain such that goƒ(x) = x = ƒog(x), we need to determine the compositions goƒ(x) and ƒog(x) separately.

First, let's find goƒ(x). The composition goƒ(x) means we need to substitute the function ƒ(x) into the function g(x).

Given that ƒ(x) = 3x + 4x - 2, we can substitute this expression into g(x) as follows:

goƒ(x) = g(3x + 4x - 2)

Next, let's find ƒog(x). The composition ƒog(x) means we need to substitute the function g(x) into the function ƒ(x).

Given that g(x) = x, we can substitute this expression into ƒ(x) as follows:

ƒog(x) = ƒ(x) = 3(x) + 4(x) - 2

Now, to find a function on a suitable domain such that goƒ(x) = x = ƒog(x), we need to equate goƒ(x) and ƒog(x) to x:

g(3x + 4x - 2) = 3(x) + 4(x) - 2

Simplifying the equation, we get:

3x + 4x - 2 = 3x + 4x - 2

Since both sides of the equation are equal, we can conclude that the function g(x) = x satisfies the condition goƒ(x) = x = ƒog(x).

Therefore, the function g(x) = x is a suitable function on the domain of real numbers such that goƒ(x) = x = ƒog(x).