# Video: Finding the Inverse Function of a Given Linear Function

Find the inverse of the function π(π₯) = 4π₯.

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### Video Transcript

Find the inverse of the function π of π₯ equals four π₯.

The inverse of a function is the opposite. In this case, π₯ is being multiplied by four. The opposite of multiplying by four is dividing by four. Therefore, at first glance, it would appear that the inverse function π minus one of π₯ is π₯ divided by four or π₯ over four.

Letβs check this answer by using a method we would use for more complicated functions. In order to work out the inverse of any function, we firstly exchange the variables and secondly rearrange the equation to express π¦ in terms of π₯. The function π of π₯ equals four π₯ can be rewritten as π¦ equals four π₯. Exchanging the variables allows us to rewrite this as π₯ equals four π¦. Dividing both sides of this equation by four gives us π¦ is equal to π₯ divided by four. Therefore, as we have rearranged it to express π¦ in terms of π₯, we can say that the inverse function π minus one of π₯ is equal to π₯ divided by four.

This confirms our initial thoughts that the inverse of the function four π₯ is π₯ divided by four.