Question

Which function below is the inverse of f(x) = The quantity of three x plus five, over seven?

A. f−1(x) = The quantity of seven x minus five, over three
B. f−1(x) = The quantity of seven x plus five, over three
C. −f−1(x) = Seven over the quantity of three x plus five
D. f−1(x) = Seven over the quantity of five minus three x

Answer 1

Given function: f(x) = (3x+5)/7

y = f(x) so it's the same as y = (3x+5)/7

Swap every copy of x and y to get x = (3y+5)/7

Solve for y to get....
x = (3y+5)/7
7x = 7*(3y+5)/7
7x = 3y+5
7x-5 = 3y+5-5
7x-5 = 3y
3y = 7x-5
3y/3 = (7x-5)/3
y = (7x-5)/3

So the inverse function is f^(-1)(x) = (7x-5)/3

Answer is choice A

Answer 2

Option A. f−1(x) = The quantity of seven x minus five, over three

Explanation:

we know that

The given function is equal to

`f(x) = (3x+5)/7`

Let

`y=f(x)`

`y= (3x+5)/7`

step 1

Exchange the variables x for y and y for x

`x= (3y+5)/7`

step 2

Isolate the variable y

`7x= (3y+5)`

`3y=7x-5`

`y=(7x-5)/3`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(7x-5)/3`