Skip to content

Course home

Sign up

Functions and Graphs

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242
Question 221

The light intensity III (in lumens) of a specialized lamp at a distance x x\,x meters is modeled by the function

I(x)=40x+3,x>0,x∈R I(x) = \frac{40}{x + 3}, \quad x > 0, x \in \mathbb{R} I(x)=x+340​,x>0,x∈R

A control system adjusts the distance x x\,x based on a setting s s\,s according to the function

g(s)=52ln⁡s,s>1,s∈R g(s) = \frac{5}{2} \ln s, \quad s > 1, s \in \mathbb{R} g(s)=25​lns,s>1,s∈R
a.

Determine, in simplest form, the value of the composite function Ig(e2)Ig(e^2)Ig(e2).

[2]
b.

Find an expression for I−1(x)I^{-1}(x)I−1(x) and state its domain.

[3]
c.

Hence, or otherwise, find all real solutions of the equation

I−1(x)=I(x) I^{-1}(x) = I(x) I−1(x)=I(x)
[4]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank