If y - fx - x - 2-x - 1 then IIT-JEE- 1984

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Standard XII

Mathematics

Complex Numbers

If y = fx =...

Question

If $y = f (x) = \frac{x + 2}{x - 1}$ then (IIT-JEE, 1984)

x = f (y)

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f (1) = 3

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y

increases with

x

for

x < 1

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f

is a rational function of

x

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Solution

The correct options are
A $x = f (y)$
D $f$ is a rational function of $x$

Suggest Corrections

Similar questions

Q. Let

f (x)

be differentiable function such that

f (\frac{x + y}{1 - x y}) = f (x) + f (y) \forall x

and

y

. If

l t x \to 0 \frac{f (x)}{x} = \frac{1}{3}

then

f (1)

equals

Q. Let f be a function satisfying the condition

λ f (x y) = \frac{f (x)}{y} + \frac{f (y)}{x}

\forall

x, y

> 0

. If

f (x)

is differentiable and

f (1) = 1

, then the value of

lim x \to \infty x

f (x)

is?

Q. Let

f (x)

be differentiable function such that

f (\frac{x + y}{1 - x y}) = f (x) + f (y) \forall x

and

y

. lf

lim x \to 0 \frac{f (x)}{x} = \frac{1}{3}

, then

f (1)

is equal to

Q. Let

f (x)

be differentiable function such that

f (\frac{x + y}{1 - x y}) = f (x) + f (y) \forall x

and

y

. lf

lim x \to 0 \frac{f (x)}{x} = \frac{1}{3}

, then

f (1)

equals

I f f : R \to R

be a function satisfying the functional Rule

f (x + f (y)) = f (x) + x + f (x - y); \forall x, y \in R

then

\begin{matrix} Column I & Column II (P) & f (0) & (A) & 1 (Q) & | f (1) + f (2) | & (B) & 3 (R) & | f (2) + f (- 3) | & (C) & 0 (S) & | f (1) + f (- 3) | & (D) & 2 \end{matrix}

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If y=f(x)=x+2x−1 then (IIT-JEE, 1984)

The correct options are A x=f(y) D f is a rational function of x

If $y = f (x) = \frac{x + 2}{x - 1}$ then (IIT-JEE, 1984)

The correct options are
A $x = f (y)$
D $f$ is a rational function of $x$