Find the inverse function. $$ f(x)=\frac{2 x+5}{4} $$ $$ f^{-1}(x)=\frac{[?] x+\square}{} $$

Question

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To find the inverse function $$ f^{-1}(x) $$ of the given function $$ f(x) = \frac{2x + 5}{4} $$, follow these steps:

1. **Start with the original function:**
   $$
   y = \frac{2x + 5}{4}
   $$

2. **Swap $$ x $$ and $$ y $$ to find the inverse:**
   $$
   x = \frac{2y + 5}{4}
   $$

3. **Solve for $$ y $$:**
   $$
   4x = 2y + 5
   $$
   $$
   2y = 4x - 5
   $$
   $$
   y = \frac{4x - 5}{2}
   $$

4. **Write the inverse function:**
   $$
   f^{-1}(x) = \frac{4x - 5}{2}
   $$

So, the inverse function is:

$$
f^{-1}(x) = \frac{4x - 5}{2}
$$

**Answer:**  
After simplifying, the inverse is (4 × x – 5) divided by 2. Thus,

f⁻¹(x) = (4x − 5)/2
The inverse function is $$ f^{-1}(x) = \frac{4x - 5}{2} $$.

Find the inverse function. \[ f(x)=\frac{2 x+5}{4} \] \( f^{-1}(x)=\frac{[?] x+\square}{} \)