Question

Let f(x) = -20x2 + 14x + 12 and g(x) = 5x - 6. Find f/g and state its domain.

Answer 1

Solution

f(x) = -20$x^{2}$ +14x + 12 and g(x) = 5x - 6.

(f/g)(x) = $\frac{f(x)}{g(y)}$

(f/g)(x) = $\frac{-20x^{2}+14x +12 }{5x - 6}$

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) = $\frac{-2 (2x +1)(5x - 6)}{(5x - 6)}$

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 :)