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f(x) = -x² + 9 is a function from ℝ to ℝ. Is it onto? Change the codomain so that it becomes onto.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

$f(x) = -x^2 + 9$ is a function from $\mathbb{R}$ to $\mathbb{R}$ . Is it onto? Change the codomain so that it becomes onto.

Need a reminder? The key ideaShow

$f$ has an inverse exactly when it is one-one and onto. To find $f^{-1}$ , solve $y = f(x)$ for $x$ . Its graph is the reflection of $f$ in $y = x$ , and $(g \circ f)^{-1} = f^{-1} \circ g^{-1}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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f(x) = -x² + 9 is a function from ℝ to ℝ. Is it onto? Change the codomain so that it becomes onto.

The worked solution

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