Respuesta :

Answer:

the inverse of the function f^-1(x)=(x-3)/(4+5x)

Step-by-step explanation:

( 3+4x)/(1-5x)

y=4x+3/1-5x swap the variables

x=4y+3/1-5y solve for y

y=x-3/4+5x

The inverse of a function is :y=x-3/4+5x

What is inverse of a function?

The inverse function returns the original value for which a function gave the output.

If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.

Steps are:

  • How do you solve inverse functions step by step?
  • Finding the Inverse of a Function
  • First, replace f(x) with y .
  • Replace every x with a y and replace every y with an x .
  • Solve the equation from Step 2 for y .
  • Replace y with f−1(x) f − 1 ( x ) .
  • Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

for example:

Suppose, f(x) = 2x + 3 is a function.

Let f(x) = 2x+3 = y

y = 2x+3

x = (y-3)/2 = f-1(y)

This is the inverse of f(x).

Given function:

f(x)= ( 3+4x)/(1-5x)

now, swap the variables x and y.

y=4x+3/1-5x

Now solving for y

x=4y+3/1-5y

y=x-3/4+5x

Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).

Learn more about inverse of a function here:

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