Question

Determine the inverse of the function RX) = 1x - 5for x2 5. Then complete the inequality for the domain restriction of the inverse function.

f(x)=
The domain restriction of f(x)is x2

Answer 1

To find the inverse of the given function f(x) = 1/x - 5, we swap x and y and solve for y. The inverse function is g(x) = 1/(x + 5). The domain restriction of the inverse function is x > 5.

Step-by-step explanation:

To determine the inverse of a function, we need to switch the roles of x and y and solve for y.

For the given function f(x) = 1/x - 5, we start by swapping x and y:

x = 1/y - 5

Next, we solve for y:

1/y - 5 = x

1/y = x + 5

y = 1/(x + 5)

So, the inverse function of f(x) is g(x) = 1/(x + 5).

The domain restriction of the inverse function is x > 5 because the original function has a restriction x > 5.