Question

What is the inverse of the function f(x) = 2x 1? • h(x) = 1 2 1 2 0 h(x)= -X 2 2 h(x) = 2 -X-2 N(x) = = -X 2

Answer 1

The inverse function of f(x) = 2x + 1 is h(x) = (x - 1) / 2. It is obtained by interchanging x and y in the original function and solving for y.

To find the inverse of the function f(x) = 2x + 1, we denote f(x) as y and interchange x and y. Then, solve for x:

y = 2x + 1

x = (y - 1) / 2

Next, interchange x and y to express y in terms of x, giving us the inverse function:

y = (x - 1) / 2

So, the inverse of f(x) = 2x + 1 is h(x) = (x - 1) / 2.

Among the given options for h(x), only h(x) = (x - 1) / 2 matches the correct inverse function. The other options do not accurately represent the inverse of the original function.