If y - f x - ax - b - b a - a - x - a - b - a - b - then f y -A- xB- - xC- 1-x-D- -1- x

The correct option is A xGiven that y=f(x)=ax b/bx a,x≠a/b, |a| ≠ |b|. ⇒ y(bx a)=ax b ⇒ byx ay=ax b ⇒ byx ax=ay b ⇒ x(by a)=ay b ⇒ x=ay b/by a=f(y) nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Function

If y = f x = ...

Question

If $y = f (x) = \frac{a x - b}{b x - a}, x \neq \frac{a}{b}, | a | \neq | b |,$ then $f (y) =$

x

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{x}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- \frac{1}{x}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $x$
Given that $y = f (x) = \frac{a x - b}{b x - a}, x \neq \frac{a}{b}, | a | \neq | b | .$
$\Rightarrow y (b x - a) = a x - b$
$\Rightarrow b y x - a y = a x - b$
$\Rightarrow b y x - a x = a y - b$
$\Rightarrow x (b y - a) = a y - b$
$\Rightarrow x = \frac{a y - b}{b y - a} = f (y)$

Suggest Corrections

Similar questions

Q. If

y = f (x) = \frac{a x - b}{b x - a}, x \neq \frac{a}{b}, | a | \neq | b |,

then

f (y) =

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

Q. If

y = \frac{a x^{2}}{(x - a) (x - b) (x - c)} + \frac{b x}{(x - b) (x - c)} + \frac{c}{x - c} + 1,

then

\frac{y^{'}}{y}

is equal to

(Here, y^{'} = \frac{d y}{d x})

Q. If x, y, z are positive real number and a, b, c are rational numbers, then the value of

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} x^{a - c}}

Q. If

x, y, z

are positive real numbers and

a, b, c

are rational numbers, then the value of

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}}

Join BYJU'S Learning Program

If y=f(x)=ax−bbx−a,x≠ab,|a|≠|b|, then f(y)=

The correct option is A xGiven that y=f(x)=ax−bbx−a,x≠ab,|a|≠|b|. ⇒y(bx−a)=ax−b ⇒byx−ay=ax−b ⇒byx−ax=ay−b ⇒x(by−a)=ay−b ⇒x=ay−bby−a=f(y)

If $y = f (x) = \frac{a x - b}{b x - a}, x \neq \frac{a}{b}, | a | \neq | b |,$ then $f (y) =$