Video: Finding the Inverse Function of a Given Linear Function

Find the inverse of the function 𝑓(π‘₯) = 4π‘₯.

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Video Transcript

Find the inverse of the function 𝑓 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 𝑓 minus one of π‘₯ is π‘₯ divided by four or π‘₯ over four.

Let’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 𝑦 in terms of π‘₯. The function 𝑓 of π‘₯ equals four π‘₯ can be rewritten as 𝑦 equals four π‘₯. Exchanging the variables allows us to rewrite this as π‘₯ equals four 𝑦. Dividing both sides of this equation by four gives us 𝑦 is equal to π‘₯ divided by four. Therefore, as we have rearranged it to express 𝑦 in terms of π‘₯, we can say that the inverse function 𝑓 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.

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