Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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 :

GinnyAnswer
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]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.