Given [tex]f(x) = 6x + 2[/tex], find [tex]f(x-3)[/tex].

A. [tex]f(x-3) = x - 1[/tex]
B. [tex]f(x-3) = 6x - 1[/tex]
C. [tex]f(x-3) = 6x^2 - 16x - 6[/tex]
D. [tex]f(x-3) = 6x - 16[/tex]



Answer :

To solve the problem, we need to find [tex]\( f(x-3) \)[/tex] for the given function [tex]\( f(x) = 6x + 2 \)[/tex].

Let's break it down step by step:

1. Substitute [tex]\( x - 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:

The function [tex]\( f(x) \)[/tex] is given as:
[tex]\[ f(x) = 6x + 2 \][/tex]
To find [tex]\( f(x-3) \)[/tex], substitute [tex]\( x-3 \)[/tex] in place of [tex]\( x \)[/tex] in the given function:
[tex]\[ f(x-3) = 6(x-3) + 2 \][/tex]

2. Distribute and simplify:

Now, distribute the 6 in the expression [tex]\( 6(x-3) \)[/tex]:
[tex]\[ f(x-3) = 6(x) - 6(3) + 2 \][/tex]
Simplify the terms inside the parentheses:
[tex]\[ f(x-3) = 6x - 18 + 2 \][/tex]
Combine the constant terms:
[tex]\[ f(x-3) = 6x - 16 \][/tex]

Therefore, the simplified expression for [tex]\( f(x-3) \)[/tex] is:
[tex]\[ f(x-3) = 6x - 16 \][/tex]

The correct answer is:
[tex]\[ f(x-3) = 6x - 16 \][/tex]