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