Question

if f(x) =a+bx / b+ax then prove that f(x) × f(1/x) =1​

Answer 1

Answer:

See explanation

Step-by-step explanation:

Given function is

              $f(x)=\dfrac{a+bx}{b+ax}$

So

           $f(\frac{1}{x})=\dfrac{a+\frac{b}{x}}{b+\frac{a}{x}}=\dfrac{\frac{ax+b}{x}}{\frac{bx+a}{x}}=\dfrac{ax+b}{bx+a}$

Replace x by $\frac{1}{x}$ and simplify

    $f(x)f(\frac{1}{x})=\dfrac{a+bx}{b+ax}\times \dfrac{ax+x}{bx+a}=1$

Hence proved