If y=f(x)= ax-b bx-a , show that x = f(y). - Vidyadip

Question

If $\text{y}=\text{f(x)}=\frac{\text{ax}-\text{b}}{\text{bx}-\text{a}},$ show that x = f(y).

✓

Answer

We have,
$\text{y}=\text{f(x)}=\frac{\text{ax}-\text{b}}{\text{bx}-\text{a}}$
$\Rightarrow\ \text{y}=\frac{\text{ax}-\text{b}}{\text{bx}-\text{a}}$
$\Rightarrow\ \text{y}(\text{bx}-\text{a})=\text{ax}-\text{b}$
$\Rightarrow\ \text{xyb}-\text{ay}=\text{ax}-\text{b}$
$\Rightarrow\ \text{xyb}-\text{ax}=\text{ay}-\text{b}$
$\Rightarrow\ \text{x}(\text{by}-\text{a})=\text{ay}-\text{b}$
$\Rightarrow\ \text{x}=\frac{\text{ay}-\text{b}}{\text{by}-\text{a}}$
$\Rightarrow\ \text{x}=\text{f(y)}$
Hence, proved.

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