Question

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

1. h(x) = one-halfx – one-half

2. h(x) = one-halfx + one-half

3. h(x) = one-halfx – 2

4. h(x) = one-halfx + 2

Answer 1

Answer:

$f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$ ⇒ answer 1

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- To find the inverse of a function :

# Write y = f(x)

# Switch the x and y

# Solve to find the new y

# The new y is $f^{-1}$

* Lets solve the problem

∵ f(x) = 2x + 1

- Put y = f(x)

∴ y = 2x + 1

- Switch x and y

∴ x = 2y + 1

- Solve to find the new y

∵ x = 2y + 1

- Subtract 1 from both sides

∴ x - 1 = 2y

- Divide both sides by 2

∴ (x - 1)/2 = y

- Divide each term in the left hand side by 2

∴ y = 1/2 x - 1/2

- Replace y by $f^{-1}$

∴ $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

* The inverse of the function is $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

Answer 2

Answer: OPTION 1

Step-by-step explanation:

Given the function f(x):

$f(x) = 2x + 1$

You can follow these steps in order to find its inverse function h(x):

- Rewrite it with $f(x)=y$:

$y= 2x + 1$

- Solve for "x":

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

- Exchange the variables:

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

- Rewrite it with $y=h(x)$. Then:

 $h(x)=\frac{1}{2}x-\frac{1}{2}$