Question

The zero of F -1(x) in F(x) = x + 3 is

-3
0
3

Answer 1

The only zero of
`F^(-1)(x)` is
`3`.

Explanation:

The function
`F^(-1)` is the inverse of function
`F`.

For a given
`x` and a given
`y`,
`F^(-1)(y) = x` if and only if
`F(x) = y`.

Let
`y` be a zero of
`F^(-1)(y)`. That is,
`F^(-1)(y) = 0`.

By the reasoning above, since
`x = 0` and this particular
`y` satisfy
`F^(-1)(y) = x`, it must be true that
`F(x) = y` for the same
`x = 0\!` and
`y\!`.

Since
`x = 0` and
`F(x) = x + 3`,
`F(0) = 3`. Therefore,
`y = F(0) = 3` since
`y = F(x)`.

Thus, the zero of
`F^(-1)(y)` would be
`y = 3`.