Let f be a real-valued invertible function such that f2x - 3x - 2 - 5x - 2- x 2- Then the value of f-113 is

F(2x 3x 2) = 5x 2 ⇒ f^ 1(5x 2) = 2x 3x 2 nbsp; Let 5x 2 = 13, then x = 3 Hence f^ 1(13) = nbsp; 2(3) 33 nbsp; 2 = 3 ...

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

Byju's Answer

Standard XII

Mathematics

Pre-Image

Let f be a re...

Question

Let $f$ be a real-valued invertible function such that $f (\frac{2 x - 3}{x - 2}) = 5 x - 2, x \neq 2.$ Then the value of $f^{- 1} (13)$ is

Open in App

Solution

$f (\frac{2 x - 3}{x - 2}) = 5 x - 2 \Rightarrow f^{- 1} (5 x - 2) = \frac{2 x - 3}{x - 2}$
Let $5 x - 2 = 13,$ then $x = 3$
Hence $f^{- 1} (13) = \frac{2 (3) - 3}{3 - 2} = 3$

Suggest Corrections

Similar questions

Let F be a real valued function of real and positive argument such that $F (x) + 3 x F (\frac{1}{x}) = 2 (x + 1) \forall x > 0$ , then the value of F(10099) is

Q. If the real-valued function

f (x) = x^{3} + 3 (a^{2} - 1) x + 1

be invertible then the set of possible real values of a is

Q. Let 'f' be real valued function such that

f (x) + 2 f (\frac{932}{x}) = 3 x

for x

\neq

0. Find f(2).___

Q. If the real valued function

f (x) = x^{3} + 3 (a^{2} - 1) x + 1

be invertible, then set of possible real values of

a

Q. If

f

is an invertible function such that

f (x) = x^{3} + e^{x / 2}

and

g (x) = f^{- 1} (x) \forall x,

then the value of

g^{'} (1)

Join BYJU'S Learning Program

Explore more

Pre-Image

Standard XII Mathematics

Join BYJU'S Learning Program

Let f be a real-valued invertible function such that f(2x−3x−2)=5x−2,x≠2. Then the value of f−1(13) is

f(2x−3x−2)=5x−2⇒f−1(5x−2)=2x−3x−2 Let 5x−2=13, then x=3 Hence f−1(13)=2(3)−33−2=3

Let $f$ be a real-valued invertible function such that $f (\frac{2 x - 3}{x - 2}) = 5 x - 2, x \neq 2.$ Then the value of $f^{- 1} (13)$ is

$f (\frac{2 x - 3}{x - 2}) = 5 x - 2 \Rightarrow f^{- 1} (5 x - 2) = \frac{2 x - 3}{x - 2}$
Let $5 x - 2 = 13,$ then $x = 3$
Hence $f^{- 1} (13) = \frac{2 (3) - 3}{3 - 2} = 3$