Question

The graph of the Function F(x) is shown below. What is the value of f^-1(1)

Answer 1

Answer:
`f^-1(1)=-1`

Explanation:

From the graph given we can derive the function
`f(x)`

`f(x) = .5x + 1.5`

To solve
`f^-1(1)` we need to find the inverse function of
`f(x)`.

Inverse functions are functions that essentially "reverse" the mapping of the domain (
`x`) and range (
`y`) of the parent function.

To find the inverse function
`f(x)` we need to solve for x in terms of y.

`y = .5x + 1.5`

`y - 1.5 = .5x`

`(y - 1.5)/(.5) = (.5x)/(.5)`

`x=2y-3`

from this, we can derive that

`f(y)^-1=2y-3`

this can also be written as a function of x

`f(x)^-1 = 2x-3`

both functions are identical.

take one of these functions and you can find that

`f^-1(1) = 2(1) - 3`

`f^-1(1) = -1`