Question

What is the inverse of g(x)= 1/x-1 and is it a function? 1/x yes 1/x 1 yes 1/x - 1 no 1/y-1 no

Answer 1

The inverse of the function g(x) = 1/(x-1) is h(x) = 1/x + 1, and it is a function.

Step-by-step explanation:

The inverse of the function g(x) = 1/(x-1) can be found by interchanging the roles of x and y and solving for y. Let's do that:

x = 1/(y-1)

Multiply both sides by (y-1):

(y-1)x = 1

Divide both sides by x:

y-1 = 1/x

Add 1 to both sides:

y = 1/x + 1

So, the inverse of g(x) is h(x) = 1/x + 1.

Now, let's check if the inverse is a function. A function is defined as a relationship where each input (x-value) corresponds to exactly one output (y-value). In this case, since g(x) is a function, its inverse h(x) will also be a function. Therefore, the inverse of g(x) is indeed a function.

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