Answer:
[tex]f^{-1}(x)=\frac{1}{2}(x-\frac{3}{5})[/tex]
Step-by-step explanation:
The given function is f(x) = 2x + [tex]\frac{3}{5}[/tex]
To get the inverse of this function we will rewrite it in the equation form.
f(x) = y = 2x + [tex]\frac{3}{5}[/tex]
Now we will replace x by y and y by x.
x = 2y + [tex]\frac{3}{5}[/tex]
In next step we have to find the value of y in terms of x.
2y = x - [tex]\frac{3}{5}[/tex]
y = [tex]\frac{1}{2}(x-\frac{3}{5})[/tex]
Now we represent y in the form of the function.
[tex]f^{-1}(x)=\frac{1}{2}(x-\frac{3}{5})[/tex]
Therefore, inverse of function f(x) is [tex]f^{-1}(x)=\frac{1}{2}(x-\frac{3}{5})[/tex]
