082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

2.3 Basic concepts of functions 57
f
f
double
double
3 6 x
2x
the input
the input
Figure2.3
Thefunction: ‘double the input’.
Thelastformisoftenwrittensimplyas f = 2x.If f (x)isafunctionofx,thenthevalue
of the function whenx = 3,forexample, iswrittenas f (x = 3) or simplyas f (3).
Example2.1 Given f (x) = 2x +1 find
(a) f(3)
(c) f(−1)
(e) f(2α)
(g) f(t+1)
(b) f(0)
(d) f(α)
(f) f(t)
Solution (a) f(3) = 2(3) +1 = 7
(b) f(0)=2(0)+1=1
(c) f(−1) =2(−1) +1 = −1
(d) f(α)isthevalueof f(x)whenxhasavalueof α,hence f(α) = 2α +1
(e) f(2α)=2(2α)+1=4α+1
(f) f(t)=2t+1
(g) f(t+1)=2(t+1)+1=2t+3
Observe from Example 2.1 that it is the rule that is important and not the letter being
used. Both f (t) = 2t + 1 and f (x) = 2x + 1 instruct us to double the input and then
add 1.
2.3.1 Argumentofafunction
Theinputtoafunctionisoftencalledtheargument.InExample2.1(d)theargumentis
α, whileinExample 2.1(e) the argument is2α.
Example2.2 Given f (x) = x , write down
5
(a) f(5x)
(b) f(−x)
(c) f(x+2) (d) f(x 2 )
Solution (a) f(5x) = 5x
5 =x (b) f(−x)=−x 5
(c) f(x+2)= x +2
5
Example2.3 Giveny(t) =t 2 +t, write down
( t
(a) y(t +2) (b) y
2)
(d) f(x 2 )= x2
5