A. x^2-3n=0 D. x^2-3x-3 R x^2-7x+5 c x^2+x-7 F. x^2-3x-7 in Fungsi invers dari f(x)=(3x+4)/(2x-1),x+(1)/(2) adal ah f^-1(x)=ldots A (2x+1)/(3x-4),xneq (4)/(3) D (2x+4)/(2x-1),x+(1)/(2) R (x+4)/(2x-3),xneq (3)/(2) E (x+4)/(2x+3),x=-(3)/(2) C. (3x-4)/(2x+1),xneq -(1)/(2)

To find the inverse of the function \( f(x) = \frac{3x+4}{2x-1} \), we need to follow these steps:<br /><br />1. **Replace \( f(x) \) with \( y \):**<br /><br /> \[<br /> y = \frac{3x+4}{2x-1}<br /> \]<br /><br />2. **Swap \( x \) and \( y \):**<br /><br /> \[<br /> x = \frac{3y+4}{2y-1}<br /> \]<br /><br />3. **Solve for \( y \):**<br /><br /> Multiply both sides by \( 2y - 1 \):<br /><br /> \[<br /> x(2y - 1) = 3y + 4<br /> \]<br /><br /> Expand the left side:<br /><br /> \[<br /> 2xy - x = 3y + 4<br /> \]<br /><br /> Rearrange terms to isolate terms involving \( y \) on one side:<br /><br /> \[<br /> 2xy - 3y = x + 4<br /> \]<br /><br /> Factor out \( y \) from the left side:<br /><br /> \[<br /> y(2x - 3) = x + 4<br /> \]<br /><br /> Solve for \( y \):<br /><br /> \[<br /> y = \frac{x + 4}{2x - 3}<br /> \]<br /><br />Thus, the inverse function is:<br /><br />\[<br />f^{-1}(x) = \frac{x + 4}{2x - 3}, \quad x \neq \frac{3}{2}<br />\]<br /><br />Therefore, the correct answer is:<br /><br />B. \(\frac{x+4}{2x-3}, x \neq \frac{3}{2}\)