Find simplified formula and domain

Question

Given S(x)=x+2 & f(x)=2x+4

So find simplified formula and Domain of v(x)=s/t(x) & w(x)=t/s(x)

Answer 1

(s/t)(x) = (x + 2)/(2x + 4)

 

This is a rational function. The domain is all x such that the denominator does not equal 0.

 

The denomination will equal 0 when 2x + 4 = 0

 

2x + 4 = 0

2x = -4

x = -2

 

The domain of (s/t)(x) is all real numbers x such that x does not equal to -2.

 

It is true that this function has a removable discontinuity at x = -2 because:

 

(x + 2)/(2x + 4) = (x + 2)/[2(x + 2)] = 1/2

 

(t/s)(x) = (2x + 4)/(x + 2)

 

Again, the denominator will equal 0 when x = -2 because if:

 

x + 2 = 0

x = -2

 

Once more, we also have a removable discontinuity because (2x + 4)/(x + 2) = 2(x + 2)/(x + 2) = 2