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If [tex]f(x+1) = x + 2[/tex], then [tex]f(x-1)[/tex] is

A. 2
B. [tex]x-1[/tex]
C. [tex]x[/tex]
D. [tex]x+1[/tex]

Sagot :

GinnyAnsweridn
To find [tex]\( f(x-1) \)[/tex], let's start by analyzing the given function [tex]\( f(x+1) = x + 2 \)[/tex].

We need to express [tex]\( f(x-1) \)[/tex] in terms of the same function. First, let’s make a substitution to simplify the problem.

Let’s set:
[tex]\[ y = x - 1 \][/tex]

So if [tex]\( y = x - 1 \)[/tex], then we can solve for [tex]\( x \)[/tex]:
[tex]\[ x = y + 1 \][/tex]

Now, substitute [tex]\( x = y + 1 \)[/tex] back into the function [tex]\( f(x+1) \)[/tex]:
[tex]\[ f((y + 1) + 1) = (y + 1) + 2 \][/tex]

This simplifies the original equation to:
[tex]\[ f(y + 2) = y + 3 \][/tex]

Next, we need to translate this back to the function we are finding, which is [tex]\( f(y) \)[/tex]. According to our substitution:
[tex]\[ y = x - 1 \][/tex]

So if we now consider [tex]\( y + 2 = (x - 1) + 2 = x + 1 \)[/tex], thus:
[tex]\[ f(x + 1) = x + 2 \][/tex]

From [tex]\( f(y + 2) = y + 3 \)[/tex], and since [tex]\( y = x - 1 \)[/tex], this translates to:
[tex]\[ f((x - 1) + 1) = x \][/tex]

So, we find that:
[tex]\[ f(x - 1) = x \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{x} \][/tex]
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