Question

What is the inverse of the function f(x) = 2x + 1?

1
1
h(x) =
X-
2
2
1
1
Oh(x) =
- x +
O h(x) =
3x-2
Oh(x) =
= {x+2
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Answer 1

`\displaystyle f^(-1)(x)= (1)/(2)x - (1)/(2)`

Explanation:

f(x) = 2x + 1

f(x) = y (output)

y = 2x + 1

Solve for x.

y - 1 = 2x

Divide 2 on both sides.

y/2 - 1/2 = x

1/2y - 1/2 = x

Switch variables.

1/2x - 1/2 = y

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

Answer 2

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

Explanation:

`f(x) = 2x+1`

Replace it with y

`y = 2x+1`

Exchange the values of x and y

`x = 2y+1`

Solve for y

`x = 2y+1`

Subtracting 1 from both sides

`2y = x-1`

Dividing both sides by 2

`y = (x-1)/(2)`

Replace it by
`f^(-1)`

So,

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