1. A function is defined by \( \mathrm{f}(x)=3 x+4 \). (a) Given that \( \mathrm{f}(k)=k \), find \( k \).

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:** \( k = -2 \)