Question

If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0? –18 –12 12 18

Answer 1

Answer:

Option 3: 12 is the correct answer.

Step-by-step explanation:

Given functions are:

$f(x) = 16x-30\\g(x) = 14x-6$

In order to find the value of x on which (f-g)(x) will be zero, first of all we have to find (f-g)(x) and then equate it equal to zero to find the value of  that will make (f-g)(x)

So,

$(f-g)(x) = f(x) - g(x)\\= (16x-30)-(14x-6)\\=16x-30-14x+6\\= 2x-24$

Now to find the value of x on which (f-g)(x) will be zero, putting (f-g)(x) = 0

$(f-g)(x) = 0\\2x-24 = 0$

Adding 24 on both sides

$2x-24+24 = 0+24\\2x = 24$

Dividing both sides by 2

$\frac{2x}{2} = \frac{24}{2}\\x = 12$

For x=12, (f-g)(x) will be zero.

Hence,

Option 3: 12 is the correct answer.