Solve for \( x \) \( f(x)=x+\frac{4}{3} \)

To solve for \( x \) in the equation \( f(x) = x + \frac{4}{3} \), we'll need to clarify the goal. Typically, "solving for \( x \)" involves finding the value of \( x \) that satisfies a particular condition for \( f(x) \). Here are a couple of possible interpretations: ### 1. Finding \( x \) When \( f(x) = 0 \) If you're looking to find the value of \( x \) that makes \( f(x) = 0 \), set the equation equal to zero and solve for \( x \): \[ f(x) = x + \frac{4}{3} = 0 \] **Steps:** \[ x + \frac{4}{3} = 0 \] \[ x = -\frac{4}{3} \] **Solution:** \[ x = -\frac{4}{3} \] ### 2. Expressing \( x \) in Terms of \( f(x) \) If you want to express \( x \) in terms of \( f(x) \), you can rearrange the original equation: \[ f(x) = x + \frac{4}{3} \] **Steps:** \[ x = f(x) - \frac{4}{3} \] **Result:** \[ x = f(x) - \frac{4}{3} \] ### 3. Finding a Fixed Point (\( f(x) = x \)) Another common interpretation is to find a fixed point where \( f(x) = x \): \[ x + \frac{4}{3} = x \] **Steps:** \[ x + \frac{4}{3} = x \] \[ \frac{4}{3} = 0 \] **Analysis:** This equation has no solution because \( \frac{4}{3} \) does not equal zero. Therefore, there is no fixed point for this function. --- **Summary:** - **If solving \( f(x) = 0 \):** \[ x = -\frac{4}{3} \] - **If expressing \( x \) in terms of \( f(x) \):** \[ x = f(x) - \frac{4}{3} \] - **If looking for a fixed point (\( f(x) = x \)):** No solution exists. If you had a different condition in mind for \( f(x) \), please provide additional details, and I'd be happy to help further!