Find the inverse of the function 𝑓(𝑥)=5𝑥+2.

Question

Find the inverse of the function 𝑓(𝑥)=5𝑥+2.

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Solution

Sure, here are the steps to find the inverse of the function 𝑓(𝑥)=5𝑥+2.

Step 1: Write down the function: 𝑓(𝑥)=5𝑥+2.

Step 2: Replace 𝑓(𝑥) with 𝑦: 𝑦=5𝑥+2.

Step 3: Swap 𝑥 and 𝑦: 𝑥=5𝑦+2.

Step 4: Solve for 𝑦:

First, subtract 2 from both sides: 𝑥-2=5𝑦.

Then, divide both sides by 5: (𝑥-2)/5=𝑦.

Step 5: Replace 𝑦 with 𝑓^(-1)(𝑥) to denote the inverse function: 𝑓^(-1)(𝑥)=(𝑥-2)/5.

So, the inverse of the function 𝑓(𝑥)=5𝑥+2 is 𝑓^(-1)(𝑥)=(𝑥-2)/5.

This problem has been solved

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