Answer:
Domain = {x | x≥0 }
Inverse = f⁻¹(x) =
.
Step-by-step explanation:
The given function is 
We know that the domain of all functions is the whole real line.
But as
.
So, the domain of f(x) is the positive real line.
Thus, the restriction to the domain of f(x) is {x | x≥0 }.
Now, we will find the inverse of f(x),

i.e. 
i.e. 
i.e. 
Hence, the inverse of f(x) is f⁻¹(x) =
.
Further, we will check the inverse using composition rule.
i.e. fοf⁻¹(x) = f⁻¹οf(x)
i.e. f(f⁻¹(x)) = f⁻¹(f(x))
i.e. f(
) = f⁻¹(
)
i.e.
= 
i.e. 0.2 × 5x = 
i.e. x = x
Hence, we get that the function
has inverse f⁻¹(x) =
.
The graph of the function and its inverse can be seen below.