Question

if f(x) = 2x+1/x-4, what is the value of f^-1 (3)?

Answer 1

=> y = (2x + 1) / (x - 4) 
=> xy - 4y = 2x + 1 
=> xy - 2x = 4y + 1 
=> x(y - 2) = 4y + 1 
=> x = (4y + 1) / (y - 2) 
=> f-1(x) = (4x + 1) / (x - 2) 
subtitute x = 3 
=> f-1(3) = 13

Answer 2

As per the inverse of a function, the value of $f^{-1}(3)$ is 13.

What is the inverse of a function?

"An inverse function is defined as a function, which can reverse into another function."

The given function is

$f(x) = \frac{2x+1}{x-4}$

⇒ $y = f(x) = \frac{2x+1}{x-4}$

⇒ $xy - 4y = 2x + 1$

⇒ $xy - 2x = 4y + 1$

⇒ $x(y - 2)= 4y + 1$

⇒ $x = \frac{4y+1}{y-2}$

⇒ $f^{-1}(x) = \frac{4y+1}{y-2}$

Now, $f^{-1}(3) = \frac{4(3)+1}{3-2} = (12+1) = 13$

Learn more about inverse of a function here: https://brainly.com/question/2541698

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