# What is the inverse function of f(x) = 1 + 4x

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f(x) = 1+4x.

We know that y = f(x) = 1+4x is bijection which is a necessary condtion for the existence of the inverse function

Let f^-1(x) be the inverse of f(x).

Then y = f^-1(x) .

So f(y) = x.

1+4y = x.

We subtract 1 from both sides.

4y = x-1

y = (x-1)/4

Therefore y = (x-1)/4 is the inverse of y = 4x+1.

The inverse function of f(x) is defined as the function which when applied to the result of f(x) gives x.

Let’s take f(x) = y = 1 + 4x

Now isolate x

y = 1 + 4x

=> y – 1 = 4x

=> [y -1] / 4 = x

Interchange x and y. y is now the inverse function of f(x) = 1+ 4x

=> y = (x -1)/4

**Therefore we have the inverse function of f(x) as (x-1)/4.**

To verify: f(x) = 1 + 4x

Applying 1 + 4x in the inverse function we have (1+ 4x – 1) / 4 = 4x / 4 = x