Question

Question 2:

Given the following functions:

f(x) = x^2

g(x) = x - 3

Find the composition of the two functions and show your process:

g(f(x))


Question 3:

If the composition of two functions is:

1
x - 3

What would be the domain restriction? Describe how you found that answer.

Answer 1

f(x) = x^2 and g(x) = x - 3.

To find f(g(x)) replace the x in f(x) by g(x).

f(g(x)) = (x - 3)^2

= x^2 - 6x + 9.

Answer 2

2:
`g(f(x))=x^2 - 3`

3: x ≠ 3

Explanation:

2 : Here the given functions,

`f(x) = x^2-----(1)`

`g(x) = x - 3----(2)`

`\because g(f(x)) = g(x^2)` ( From equation (1) ),

`=x^2-3` ( From equation (2) )

3 :

`h(x) = (1)/(x-3)`

Since, it is a rational function,

A rational function is defined for all real numbers except those for which,

Denominator = 0,

If x - 3 = 0

⇒ x = 3

So, Domain of h(x) = R - {3}

i.e., the domain restriction for h(x) is x ≠ 3