Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

If [tex]f(x) = 16x - 30[/tex] and [tex]g(x) = 14x - 6[/tex], for which value of [tex]x[/tex] does [tex](f - g)(x) = 0[/tex]?

A. -18
B. -12
C. 12
D. 18

Sagot :

To determine the value of [tex]\( x \)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex], we start by defining the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

[tex]\[ f(x) = 16x - 30 \][/tex]
[tex]\[ g(x) = 14x - 6 \][/tex]

Next, we need to find [tex]\((f - g)(x)\)[/tex], which is the difference between [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]

Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

[tex]\[ (f - g)(x) = (16x - 30) - (14x - 6) \][/tex]

Simplify the expression inside the parentheses:

[tex]\[ (f - g)(x) = 16x - 30 - 14x + 6 \][/tex]

Combine like terms:

[tex]\[ (f - g)(x) = (16x - 14x) + (-30 + 6) \][/tex]

[tex]\[ (f - g)(x) = 2x - 24 \][/tex]

We are given that [tex]\((f - g)(x) = 0\)[/tex]. Therefore, we set the expression equal to zero and solve for [tex]\( x \)[/tex]:

[tex]\[ 2x - 24 = 0 \][/tex]

Add 24 to both sides of the equation:

[tex]\[ 2x = 24 \][/tex]

Divide both sides by 2 to solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{24}{2} \][/tex]

[tex]\[ x = 12 \][/tex]

Thus, the value of [tex]\( x \)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex] is [tex]\( \boxed{12} \)[/tex].