Question
1. A function is defined by \( \mathrm{f}(x)=3 x+4 \). (a) Given that \( \mathrm{f}(k)=k \), find \( k \).
Ask by Ray Lindsey. in Namibia
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( k = -2 \)
Solution
To find the value of \( k \) such that \( \mathrm{f}(k) = k \) for the function \( \mathrm{f}(x) = 3x + 4 \), follow these steps:
1. **Set Up the Equation:**
\[
\mathrm{f}(k) = k
\]
Substitute the function into the equation:
\[
3k + 4 = k
\]
2. **Solve for \( k \):**
\[
3k + 4 = k
\]
Subtract \( k \) from both sides:
\[
3k - k + 4 = 0
\]
Simplify:
\[
2k + 4 = 0
\]
Subtract 4 from both sides:
\[
2k = -4
\]
Divide both sides by 2:
\[
k = -2
\]
**Final Answer:**
\( k = -2 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve \( \mathrm{f}(k) = k \) given the function \( \mathrm{f}(x) = 3x + 4 \), we substitute \( k \) into the function: \[ 3k + 4 = k \] Now, we can rearrange the equation: \[ 3k - k + 4 = 0 \implies 2k + 4 = 0 \] Solving for \( k \): \[ 2k = -4 \implies k = -2 \] Thus, the value of \( k \) is \(-2\).
