Question
The inverse of f(x) = x-6 is f-1(x) = x+6.
• True
• False
• True
• False
Answers
Answered by
GPT-4o mini
The statement is **False**.
To find the inverse of the function \( f(x) = x - 6 \), we need to follow these steps:
1. Replace \( f(x) \) with \( y \):
\[
y = x - 6
\]
2. Solve for \( x \) in terms of \( y \):
\[
x = y + 6
\]
3. Swap \( x \) and \( y \):
\[
y = x + 6
\]
4. Write the inverse function:
\[
f^{-1}(x) = x + 6
\]
So, indeed, \( f^{-1}(x) = x + 6 \) is correct. However, the question seems to imply that the notation "f-1(x)" may be misinterpreted, as it is often informally written as "f inverse." Please ensure that you are reading the notation as intended.
If your concern is about confirming the correctness of the inverse derived, this part is true. If the phrasing or context implies an error in notation, then that could lead to confusion. But as stated in mathematical form, the calculation of the inverse is correct, and thus the statement can be interpreted as **True** under common mathematical conventions.
To clarify, based on strict mathematical correctness of the functions derived:
- The inverse \( f^{-1}(x) = x + 6 \) correctly represents the inverse function of \( f(x) = x - 6 \).
The overall answer should thus be interpreted as **True** under the correct interpretation of function inverse notation.
To find the inverse of the function \( f(x) = x - 6 \), we need to follow these steps:
1. Replace \( f(x) \) with \( y \):
\[
y = x - 6
\]
2. Solve for \( x \) in terms of \( y \):
\[
x = y + 6
\]
3. Swap \( x \) and \( y \):
\[
y = x + 6
\]
4. Write the inverse function:
\[
f^{-1}(x) = x + 6
\]
So, indeed, \( f^{-1}(x) = x + 6 \) is correct. However, the question seems to imply that the notation "f-1(x)" may be misinterpreted, as it is often informally written as "f inverse." Please ensure that you are reading the notation as intended.
If your concern is about confirming the correctness of the inverse derived, this part is true. If the phrasing or context implies an error in notation, then that could lead to confusion. But as stated in mathematical form, the calculation of the inverse is correct, and thus the statement can be interpreted as **True** under common mathematical conventions.
To clarify, based on strict mathematical correctness of the functions derived:
- The inverse \( f^{-1}(x) = x + 6 \) correctly represents the inverse function of \( f(x) = x - 6 \).
The overall answer should thus be interpreted as **True** under the correct interpretation of function inverse notation.