Question

What is the inverse of f(x)=4x+3 ?
f−1(x)=4x−3
f−1(x)=1/4x−3//4
f−1(x)=−4x−3
f−1(x)=−1/4x+3/4

Answer 1

Steps:

Here are the steps to convert an equation to its inverse:

1. Change f(x) to y
2. Switch the positions of x and y
3. Solve for y
4. Change y to f^-1(x)

Firstly, do the first two steps:

$x=4y+3$

Next, let's solve for y. Subtract 3 on both sides:

$x-3=4y$

Next, divide both sides by 4:

$\frac{1}{4}x-\frac{3}{4}=y$

Answer:

Finally, change y to f^-1(x) and your final answer will be:

$f^{-1}(x)=\frac{1}{4}x-\frac{3}{4}$ , or the second option.

Answer 2

The inverse of f(x) is $\rm f^{-1}(x) = \dfrac{1}{4}x-\dfrac{3}{4}$.

Given that

Function; $\rm f(x)=4x+3$

We have to determine

The inverse of f(x).

According to the question

To determine the inverse of f(x) following all the steps given below.

Let the function f(x) = x then $\rm f^{-1}x = x$,

Then,

$\rm \rm f(x)=4x+3\\\\x =4f^{-1}(x)+3\\\\x-3 = 4f^{-1}(x)\\\\f^{-1}(x) = \dfrac{x-3}{4x}\\\\f^{1} (x)= \dfrac{x}{4} - \dfrac{3}{4}\\\\f^{-1}(x) = \dfrac{1}{4}x-\dfrac{3}{4}$

Hence, The inverse of f(x) is $\rm f^{-1}(x) = \dfrac{1}{4}x-\dfrac{3}{4}$.

To know more about Inverse Function click the link given below

https://brainly.com/question/1921243