The inverse of g(x) is a function. true or false.

The correct choice is B. FALSE

Step-by-step explanation:

Given the function G(x)

Now, to check whether the inverse of G(x) exists or not :

We first check if G(x) is one-one and onto because a function has inverse if and only if the function is one-one and onto.

Now, First to check G(x) is one-one graphically : We use horizontal line test which states that every horizontal line must intersect the graph of the function at at most one point.

But in the given graph if we take horizontal line to be y = 0 then it intersects the graph at 3 points

⇒ we get same images at different values of x. So, G(x) is not one-one

Hence, inverse of G(x) does not exist and as a result cannot be function.

Therefore, The correct choice is B. FALSE