Written Assignment unit 4

1. What can be said about the domain of the function f ∘ g where f (y) = 4/y-2 and

g (x) = 5/3x-1? Express it in terms of a union of intervals of real numbers. Go to

www.desmos.com/calculator and obtain the graph of f, g, and f ∘ g.


f∘g = 4
5- 2
3x - 1
The domain of the function in this rational expression
signifies that the denominator should not be zero. X
= 4 can take any vale or real number except 7/6
5- 2
3x – 1 1
In this case y = f (t)
5 – 2(3x – 1)
f (y) = 4/y-2 = y= f (t)
3x – 1
g (x) = 5/3x-1

= 4 f ∘ g = 4 (3x – 1) = 12x – 4

5 – 6x + 2 7 – 6x 7 – 6x

3x – 1
Expression in terms of union of intervals of real
= 4 number:
7 – 6x (−∞, 7/6) ∪ (7/6,∞)
3x – 1

= 4 (3x – 1)
7 – 6x