If f x - ax - x -1- x -1- then- for what value of a is f f x - xA- -2B- -2C- 1D- -1

The correct option is D 1f(f(x))=af(x)/f(x)+1=a(az/z+1)/(az/z+1+1)=a^2.x/ax+x+1 ∴ x=a^2 . x/(a+x)x+1 or x((a +1)x+1 a^2)=0 Or (a+1)x^2+(1 a^2)x=0. This shou ...

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

Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

If f x = ax /...

Question

If $f (x) = \frac{a x}{x + 1}, x \neq - 1$ . then, for what value of a is f(f(x)) = x

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

-1

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

Open in App

Solution

The correct option is D -1
$f (f (x)) = \frac{a f (x)}{f (x) + 1} = \frac{a (\frac{a z}{z + 1})}{(\frac{a z}{z + 1} + 1)} = \frac{a^{2} . x}{a x + x + 1}$

$∴ x = \frac{a^{2} . x}{(a + x) x + 1}$ or $x ((a + 1) x + 1 - a^{2}) = 0$

Or $(a + 1) x^{2} + (1 - a^{2}) x = 0$ . This should hold for all x.

$\Rightarrow a + 1 = 0, 1 - a^{2} = 0, ∴ a = - 1.$

Suggest Corrections

Similar questions

Q. Let

f (x) = \frac{α x}{x + 1}, x \neq - 1

. Then, for what value of α is

f (f (x)) = x ?

(a)

\sqrt{2}

(b)

- \sqrt{2}

Q. Let

f (x) = \frac{a x}{x + 1}

, where

x \neq - 1

. Then for what value of

a

f (f (x)) = x

always true

Let $f (x) = \frac{α x}{x + 1}, x \neq - 1$ . Then write the value of $α$ satisfying $f (f (x)) = x$ for all $x \neq - 1$ .

If $f (x) = \frac{α x}{x + 1}, x \neq - 1$ then , for what value of $α$ is $f (f (x)) = x$

If x = √2+√1, then the value of $[x + \frac{1}{x}]$ is ?

Join BYJU'S Learning Program

If f(x)=axx+1,x≠−1 . then, for what value of a is f(f(x)) = x

The correct option is D -1f(f(x))=af(x)f(x)+1=a(azz+1)(azz+1+1)=a2.xax+x+1 ∴x=a2.x(a+x)x+1 or x((a+1)x+1−a2)=0 Or (a+1)x2+(1−a2)x=0. This should hold for all x. ⇒a+1=0,1−a2=0, ∴a=−1.

If $f (x) = \frac{a x}{x + 1}, x \neq - 1$ . then, for what value of a is f(f(x)) = x