Question

Question 2:

Answer 1

Answer:

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

3: x ≠ 3

Step-by-step 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 :

$h(x) = \frac{1}{x-3}$

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

Answer 2

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.