Q:

Let f(x) = -20x^2 + 14x + 12 and g(x) = 5x- 6. Find f/g and state its domain

Accepted Solution

A:
f(x) = -20xΒ²+14x+12 and g(x) = 5x-6

[tex] \frac{f(x)}{g(x)} = \frac{-20 x^{2} + 14x+12}{5x-6} [/tex]
[tex]= \frac{-(20 x^{2} -14x-12)}{5x-6} [/tex]
[tex] \frac{-[20 x^{2}-24x+10x-12] }{5x-6} [/tex]
=[tex] \frac{-[2x(10x-12)+1(10x-12)]}{5x-6} [/tex]
=[tex] \frac{-[(2x+1)(10x-12)]}{5x-6} [/tex]
=[tex] \frac{-2(2x+1)(5x-6)}{5x-6} [/tex]
=[tex]-2(2x+1)[/tex]

Now, since this is a linear equation, it is defined at every real number.
Therefore, domain is x∈(⁻∞,⁺∞)