1. 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 \(x^2+2x+2\)?