Question

Two functions are defined as follows: f : x → 2x - 3 and g : x → x2 - 1

(i) Calculate f(5)
(ii) g( - 3) =
(iii) fg(x)=
(iv)gf(x)=
(v) f-1(x)=

Answer 1

f(5) = 2(5)-3 = 7
g(-3) = (-3)2-1 = -7
fg(x) = f(2x-1) = 2(2x-1)-3 = 4x-2-3 = 4x-5
gf(x) = g(2x-3) = 2(2x-3)-1 = 4x-6-1 = 4x-7

let y=f(x)
y=2x-3
make x the subject,
2x=y+3
x = (y+3)/2
f-1(y) = (y+3)/2
f-1(x) = (x+3)/2