Question

given the function f(x) = the quantity of 5x minus 3, divided by 4, which of the below expressions is correct? a. f−1(x) = the quantity of 3 minus 5x, divided by 4 b. f−1(x) = the quantity of 4x plus 3, divided by 5 c. f−1(x) = the quantity of 4x minus 3, divided by 5. d. f−1(x) = the quantity of negative 5x minus 3, divided by 4.

Answer 1

Option B. will be the answer.

Explanation:

The given function is f(x) =
`(5x-3)/(4)`

Now we have to find the inverse function
`f^(-1)(x)` of the given function.

We can rewrite the function in the form of an equation.

y =
`(5x-3)/(4)`

Now flip x by y and y by x.

x =
`(5y-3)/(4)`

Now solve this equation for the value of y

5y - 3 = 4x

5y = 4x + 3

y =
`((4x+3))/(5)`

Now rewrite the equation in the form of a function which will the inverse of the parent function.

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

Therefore, Option B. is the answer.

Answer 2

`f(x)= (5x-3)/(4) \\ y= (5x-3)/(4) \\ 4y=5x-3 \\ 4y+3=5x \\ x= (4y+3)/(5) \\ f^(-1) (x)=(4x+3)/(5)`