Question

The zero of F -1(x) in F(x) = x + 3 is -3 0 3

Answer 1

Answer:

The only zero of $F^{-1}(x)$ is $3$.

Step-by-step 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 $y = 3$.