F(x)=2x+1 and g(x)= x^2-4x+3

Question

find the domain of g(x)/f(x) and f(x)/g(x)? 

 

Answer 1

Domain :

Domain of a function f(x) is set of those values of x which will make the function mathematically legal or correct..certain operations like division by zero , square root of a negative number do not exist in real maths.

1. Domain excludes x - values that result in division by zero.

2. Domain excludes x - values that result in even roots of negative numbers.

The functions are f (x) = 2x + 1 and g (x) = x² - 4x + 3.

• g (x) / f (x) = (x² - 4x + 3)/(2x + 1).

Find the factors of numerator expression x² - 4x + 3.

x² - 4x + 3

= x² - 3x - x + 3

= x(x - 3) - 1(x - 3)

= (x - 3)(x - 1).

g(x) / f (x) = [(x - 3)(x - 1)] / (2x + 1).

The denominator expression is (2x + 1) and it is equals to zero.

(2x + 1) = 0

2x = - 1

x = - 1/2.

The denominator is zero, when x = - 1/2.

Domain excludes x - values that result in division by zero.

The function has an implied domain that consists of all real x other than x = - 1/2.

These values are excluded from the domain because division by zero is undefined.

Domain : {x Є R : x ≠ - 1/2}.

• f (x) / g (x) = (2x + 1)/(x² - 4x + 3).

Find the factors of denominator expression x² - 4x + 3.

x² - 4x + 3

= x² - 3x - x + 3

= x(x - 3) - 1(x - 3)

= (x - 3)(x - 1).

f(x) / g(x) = (2x + 1) / [(x - 3)(x - 1)].

The denominator expression is (x - 3)(x - 1) and it is equals to zero.

(x - 3)(x - 1) = 0

x = 3 and x = 1.

The denominator is zero, when x = 3 and x = 1.

Domain excludes x - values that result in division by zero.

The function has an implied domain that consists of all real x other than x = 3 and x = 1.

These values are excluded from the domain because division by zero is undefined.

Domain : {x Є R : x ≠ 1 and x ≠ 3}.