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Find the range of y=\frac{3x+4}{2x-1}

Option: 1

R

 


Option: 2

R-\left \{ \frac{3}{2} \right \}


Option: 3

R-\left \{ 1 \right \}


Option: 4

\Phi


Answers (1)

best_answer

We can first write y=f(x)  in terms of x = g(y)

Then the domain of x=g(y) is same as range of y=f(x)
\begin{aligned} & y=\frac{3 x+4}{2 x-1} \\ \Rightarrow & 2 x y-y=3 x+4 \\ \Rightarrow & 2 x y-3 x=y+4 \\ \Rightarrow & x=\frac{y+4}{2 y-3} \end{aligned}

Now domin of this will not include y when 2y-3=0\Rightarrow y=\frac{3}{2}

Domain of x=g\left (y \right ) is y\in R-\left \{ \frac{3}{2} \right \}

So, range of y=\frac{3x+4}{2x-1} is y\in R-\left \{ \frac{3}{2} \right \}

Posted by

SANGALDEEP SINGH

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