Question

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Let the function f: R – (4/3)→ R – (4/3) is defined by f(x) = (4x+3)/(3x+4). Prove that the given function is bijective. And, find the inverse of the function and f-1(0) and the value of x, such that f-1(x) = 2.​

Answer 1

Answer:

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Answer 2

ANSWER:-

It is given that f : R → R given by f (x) = 4x + 3

Let x,y ∈ R such that f(x) = f(y)

⇒ 4x +3 = 4y +3

⇒ 4x = 4y

⇒ x = y

therefore,  f is one- one function.

Now, for y ∈ R, Let y = 4x +3

∈ R

⇒ for any y ∈ R, there exists x = ∈ R

such that, f(x) =

⇒ F is onto function.

Since, f is one –one and onto

therefore , f is inversible.

now, f(x) = 4x + 3

f(x) = y = 4x + 3

y = 4x + 3

=> y - 3 = 4x

=> 4x = (y - 3)

=> x = (y - 3)/4

=> f(y) = (y - 3)/4

here f(y) is not other than inverse of f(x)

put x in place of y and write f(y) = f⁻¹(x)

e.g., f⁻¹(x) = (x -3)/4

hence, inverse of f(x) = (x-3)/4