Understanding Engineering Mathematics

3.1.5 Composition of functions ➤97 108➤➤

Iff(x)=x+1andg(x)=

1

x− 1

express in their simplest form:

(i) f(g(x)) (ii) g(f(x))

3.1.6 Inequalities ➤97 109➤➤

Find the range of values ofxfor which

1 < 4 x− 3 < 4

3.1.7 Inverse of a function ➤100 109➤➤

Find the inverse function of the function

f(x)=

x

x− 1

x= 1

3.1.8 Series and sigma notation ➤102 109➤➤

Write out the following series in full

∑^6

r= 1

r

r+ 1

3.1.9 Finite series ➤103 109➤➤

Sum the finite geometric series

1

2

+

1

22

+

1

23

+

1

24

+

1

25

3.1.10 Infinite series ➤105 110➤➤

Sum the infinite geometric series

1

2

+

1

22

+

1

23

+···

3.1.11 Infinite binomial series ➤106 110➤➤

Find the first four terms of the binomial expansion of (1+ 3 x)−^2.