Answer: [tex]\bold{(D)\ f^{-1}(x)=\dfrac{2x+3}{4}}[/tex]
Step-by-step explanation:
When finding the inverse, swap the x's and y's and solve for y.
[tex]f(x)=\dfrac{4x-3}{2}\\\\y = \dfrac{4x-3}{2}\ \quad \rightarrow \quad \text{f(x) is also called y}\\\\x = \dfrac{4y-3}{2}\ \quad \rightarrow \quad \text{swapped the x and y}\\\\2x=4y-3\ \quad \rightarrow \quad \text{multiplied both sides by 2}\\\\2x+3=4y\ \quad \rightarrow \quad \text{added 3 to both sides}\\\\\dfrac{2x+3}{4}=y\ \quad \rightarrow \quad \text{divided both sides by 4}\\\\f^{-1}(x)=\dfrac{2x+3}{4}\ \quad \rightarrow \quad \text{y is the inverse}\ [f^{-1}(x)][/tex]
