Quadratic Functions Structured Questions | Cambridge IGCSE Additional Mathematics

Question 1 of 5 · 9 marks

Quadratic Functions · Range & Inverse Functions

4 parts

Additional Mathematics 0606 · Question 1Paper 2 · Calculator[9 marks]

The function $f$ is defined by $f(x) = 4x - x^2$ for $x \in \mathbb{R}, x \geq 1$ .

(a)

Express $f(x)$ in the form $k - (x-h)^2$ , stating the constants $h$ and $k$ .

[2]

(b)

State the range of $f$ .

[2]

(c)

Explain why $f$ does not have an inverse.

[2]

(d)

Given that $g(x) = 4x - x^2$ for $x \geq c$ , state the smallest value of $c$ for which $g^{-1}$ exists, and find an expression for $g^{-1}(x)$ .

[3]