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lukranit [14]
3 years ago
14

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

Mathematics
2 answers:
Luda [366]3 years ago
7 0

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}

andreyandreev [35.5K]3 years ago
6 0

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}

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Step-by-step explanation:

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