IB Maths AI HL AI 2.1 practice question

Paper 1Easy5 marks

A positioning device converts a control setting $x$ to an output $f(x)$ Figure 1 shows its calibration curve. The rule is

f(x)=(x-3)^2-2

on the branch shown. Both $x$ and $f(x)$ are measured in device units.

(a)

Use Figure 1 to write down the range of $f$

[1]

(b)

Find $f^{-1}(x)$

[1]

(c)

State the domain of $f^{-1}$

[1]

(d)

Complete each statement, including the appropriate domain for $x$

(i)

$(f\circ f^{-1})(x)=\dots$

[1]

(ii)

$(f^{-1}\circ f)(x)=\dots$

[1]