Question

What is the inverse of the function

Answer 1

Answer:

1/2x -1/2

Step-by-step explanation:

f(x) = 2x+1

y = 2x+1

Switch x and y

x = 2y+1

Solve for y

Subtract 1

x-1 = 2y+1-1

x-1 =2y

Divide by 2

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

1/2x -1/2 = y

The inverse is 1/2x -1/2

Answer 2

Answer:

$\huge\boxed{h(x) = \frac{1}{2} x - \frac{1}{2}}$

Step-by-step explanation:

$f(x) = 2x+1$

Put f(x) = y

$y = 2x + 1$

Interchange x and y

$x = 2y+1$

Solve for y

$x = 2y+1$

Subtracting 1 to both sides

$x-1 = 2y$

Dividing both sides by 2

$\frac{x-1}{2} = y \\\\ OR\\\\ y = \frac{x-1}{2}$

Put y = h(x)

$\bold{h(x) = \frac{1}{2} x - \frac{1}{2}}$