Subgraph one to one

[dookiwoo]

so stumped -
so
f(x)=(x+2)^2 - 1
question: if h(x) is a subgraph of f(x) such that h(x) is a one to one function, find the maximal domain of h(x)

i dont even know how to find h(x), ive graphed f(x) and its not one to one so i dont understand how to find h(x)
also the next question is to find the inverse function of h(x) but i dont even know what h(x) is so any help would be greatly appreciated

 

[BigBeachBanana]

subgraph

I'm not familiar with this term. A google search reveals a definition in Graph Theory, which is not what the problem refers to. Can you define "subgraph"?

 

[Otis]

h(x) is a subgraph of f(x) such that h(x) is a one to one function, find the maximal domain of h(x)

Hi dookiwoo. I've seen "subgraph" in geometry before, but in this exercise it seems to mean a section of the graph of f(x). Does your textbook define subgraph?

The maximal domain requirement would mean choosing a one-to-one subgraph that has the biggest domain. If my assumption above is correct, then there are two sections of f(x) from which to choose for h(x). Function f is a quadratic polynomial whose graph has a well-known shape, yes?

 

[mario99]

If I were you, I would find the inverse of $h(x)$ first.

Let $\ \ y = (x + 2)^2 - 1$

Solve for $x$, you will get two functions. One function has a positive square root and one function has a negative square root. If you choose the positive root, then your $h(x)$ is the right half of $f(x)$. If you choose the negative root, then your $h(x)$ is left half of $f(x)$.

 

[BigBeachBanana]

I would find the inverse of $h(x)$ first.

Before one can find something, one must know what one is looking for.
What is a subgraph?

 

[Steven G]

You have the graph of f(x), good. You already stated that f(x) is NOT one to one.
Now you need to remove the smallest possible portion of the graph of f(x) so that what remains IS a one to one function. This new graph is h(x). Please note that different students will get different results for h(x) as they removed different portions of f(x) to get a one to one function.
Now given your graph of h(x) state the domain.