Solution
f(x) = -20[tex]x^{2}[/tex] +14x + 12 and g(x) = 5x - 6.
(f/g)(x) = [tex]\frac{f(x)}{g(y)}[/tex]
(f/g)(x) = [tex]\frac{-20x^{2}+14x +12 }{5x - 6}[/tex]
Step 1: Now we have to factorize the numerator.
f(x) = -20x^2 + 14x + 12
Factor out -2, we get
= -2 (10x^2 - 7x - 6)
Now we can factorize 10x^2 - 7x - 6
f(x) = -2(2x + 1) (5x - 6)
Step 2: Plug in the factors
(f/g)(x) = [tex]\frac{-2 (2x +1)(5x - 6)}{(5x - 6)}[/tex]
Step 3: Cancel out the common factor (5x - 6) from the numerator and the denominator, we get
(f/g)(x) = -2(2x +1) = -4x -2
Since -4x -2 is linear expression, the domain is all the real numbers.
Therefore, the answer is –4x – 2; all real numbers
Thank you :)
