Question

I need help with this question

Answer 1

Answer:

Option B is correct

Step-by-step explanation:

Given:

f(x) = -20x^2 +14x +12 and

g(x) = 5x - 6

We need to find f/g and state its domain.

f/g = -20x^2 +14x +12/5x - 6

Taking -2 common from numerator:

f/g = -2(10x^2 - 7x - 6) / 5x -6

Factorize 10x^2 - 7x - 6= 10x^2 - 12x +5x -6

Putting in the above equation

f/g = -2(10x^2 - 12x +5x -6)/ 5x -6

f/g = -2(2x(5x-6) + 1 (5x-6)) / 5x-6

f/g = -2 ( (2x+1)(5x-6))/5x-6

cancelling 5x-6 from numerator and denominator

f/g = -2(2x+1)

f/g = -4x -2

The domain of the function is set of all values for which the function is defined and real.

So, our function g(x) = 5x -6 and domain will be all real numbers except x = 6/5 as denominator will be zero if x=5/6 and the function will be undefined.

So, Option B is correct.

Answer 2

ANSWER

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

Option B is correct.

EXPLANATION

The given functions are:

$f(x) = - 20 {x}^{2} + 14x + 12$

We factor to get,

$f(x) = - 2(10 {x}^{2} - 7x - 6)$

Split the middle term:

$f(x) = - 2(10 {x}^{2} + 5x - 12x - 6)$

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

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

and

$g(x) = 5x - 6$

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

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

where 5x-6≠0

x≠6/5

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

Cancel the common factors to get,

$( \frac{f}{g} ) = - 2(2{x} + 1)$

$( \frac{f}{g} ) = - 4{x} - 2$