Skip to content

Course home

1.5 B: Algebra and functions

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354
Question 225

The function fff is defined by

f(x)=∣x−12∣+15 for x∈R f(x) = |x - 12| + 15 \text{ for } x \in \mathbb{R} f(x)=∣x−12∣+15 for x∈R

The function ggg is defined by

g(x)=e2x+15 g(x) = e^{2x} + 15 g(x)=e2x+15

where ggg has its greatest possible domain.

a.

Using set notation, state the range of fff.

[1]
b.

State the domain of ggg.

[1]
c.

The composite function hhh is given by

h(x)=fg(x) for x∈domain of g h(x) = f g(x) \text{ for } x \in \text{domain of } g h(x)=fg(x) for x∈domain of g

(i) Write down an expression for h(x)h(x)h(x) in terms of xxx. (ii) Determine if hhh has an inverse. Fully justify your answer.

[3]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank