Question

Which function below is the inverse of f(x) = the quantity of two x plus three, over five.?f−1(x) = the quantity of five x plus three, over twof−1(x) = the quantity of five x minus three, over twof−1(x) = five over the quantity of two x plus threef−1(x) = five over the quantity of three minus two x?

Answer 1

Original function: f(x)=(2x+3)/5
[change f(x) to y]: y=(2x+3)/5
[swap x and y]: x=(2y+3)/5
[solve again for y]: 5x=2y+3
y=(5x-3)/2
f-1(x) = (5x-3)/2..."The quantity five x minus three, over two

Answer 2

`f^(-1)(x)=(5x-3)/(2)`

f⁻¹(x) = the quantity of five x minus three, over two

C is correct

Explanation:

Given:
`f(x)=(2x+3)/(5)`

We need to find inverse of function f(x)

Step 1: Set f(x)=y

`y=(2x+3)/(5)`

Step 2: Switch x and y

`x=(2y+3)/(5)`

Step 3: Solve for y (isolate y)

`5x=2y+3`

`2y=5x-3`

`y=(5x-3)/(2)`

Therefore,
`f^(-1)(x)=(5x-3)/(2)`

Now we write as sentence form,

Inverse of f(x) is 5 times of x minus 3 over 2.

Hence, f⁻¹(x) = the quantity of five x minus three, over two