- The function \(f\) from \(\mathbb{R}\) to \(\mathbb{R}\) is given by \(f: x\mapsto x^2+2x+2\). Find the range of \(f\), and state, with a reason, whether or not \(f\) is bijective.

To explain, the symbol \(\mathbb{R}\) denotes the set of all real numbers, that is, the set of all numbers on the number line.

We’re definitely going to need to understand the word *bijective* for this question. Click on the link in the question above for a careful explanation.

The notation \(f \circ g\) means ‘the function \(g\) followed by the function \(f\)’, or ‘\(f\) composed with \(g\)’.

Could we complete the square on \(x^2+2x+2\)?