The function $f\,$ is defined by

$f(x) = (x - 3)^2 + 1$ for $\geq k\,$

where $k\,$ is a constant.

Given that $f^{-1}$ exists, state the least possible value of $k$ .

In parts (b) to (d), $k\,$ takes this least possible value.

Evaluate $f f (6)$ .

Solve the equation $f (x) = x$ .

Explain why your answer to part (c) is also the solution of the equation $f(x) = f^{-1}(x)$ .

The function $f\,$ is defined by

$f(x) = (x - 3)^2 + 1$ for $\geq k\,$

where $k\,$ is a constant.

Given that $f^{-1}$ exists, state the least possible value of $k$ .

In parts (b) to (d), $k\,$ takes this least possible value.

Evaluate $f f (6)$ .

Solve the equation $f (x) = x$ .

Explain why your answer to part (c) is also the solution of the equation $f(x) = f^{-1}(x)$ .

3 Unit A2 1: Pure Mathematics (A-level only)

3 Unit A2 1: Pure Mathematics (A-level only) Questions