2.7 Composite and inverse functionsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.7 Composite and inverse functions

1. $f(x)=2x+3$ and $g(x)=x^2$, for $x\in\mathbb{R}$.
   Solve $(f\circ g)(x)=11$.2 marks
2. The fare in EUR for a taxi journey of $d$ km is $f(d)=3+1.2d$, for $d\geq0$. Fares are converted to AED using $g(x)=4x$.
   A passenger is charged 96 AED. Find the distance of the journey.2 marks
3. $f(x)=(x-3)^2-2$, defined for $x\in\mathbb{R}$.
   (i) Explain why $f$ has no inverse function on the given domain. (ii) State the largest domain of the form $x\geq k$ on which $f$ has an inverse, and the range of $f$ on this domain.3 marks