find the range of the function 3x+5÷4x-7

Dear Student ,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{Let} \mathrm{y}=\frac{3\mathrm{x}+5}{4\mathrm{x}-7} \\ 4\mathrm{xy} - 7\mathrm{y} = 3\mathrm{x} + 5 \\ 4\mathrm{xy} - 3\mathrm{x} = 5 + 7\mathrm{y} \\ \mathrm{x} \left( 4\mathrm{y}-3 \right) = 5 + 7\mathrm{y} \\ \mathrm{x} = \frac{5+7\mathrm{y}}{4\mathrm{y}-3} \\ \mathrm{For} \mathrm{x} \mathrm{to} \mathrm{be} \mathrm{defined}, \\ 4\mathrm{y}-3\ne 0 \\ 4\mathrm{y}\ne 3 \\ \mathrm{y}\ne \frac{3}{4} \\ \mathrm{Range} = \mathrm{R} - \left\{\frac{3}{4}\right\} \end{gathered}$$

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