Question

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

–4x – 2; all real numbers

5x - 6; all real numbers except x = 6/5

–4x – 2; all real numbers except x = 6/5

5x - 6; all real numbers

Answer 1

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

(f/g)(x) =
`(f(x))/(g(y))`

(f/g)(x) =
`(-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) =
`(-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 :)