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Show that f(x) = 4 - 3x is one-one. Show that g(x) = x² + 6x is not one-one on ℝ.

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

Show that $f(x) = 4 - 3x$ is one-one.

Show that $g(x) = x^2 + 6x$ is not one-one on $\mathbb{R}$ .

Find a domain on which $g$ is one-one.

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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Show that f(x) = 4 - 3x is one-one. Show that g(x) = x² + 6x is not one-one on ℝ.

The worked solution

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