#!/usr/bin/env julia

# Jacek Poziemski 272389

"""
    f(x::Float64)::Float64

Calculate `sqrt(x^2 + 1) - 1`.

# Arguments
- `x::Float64`: function argument
"""
f(x::Float64)::Float64 = sqrt(x^2 + one(Float64)) - one(Float64)

"""
    g(x::Float64)::Float64

Calculate `x^2 / (sqrt(x^2 + 1) + 1)`.

# Arguments
- `x::Float64`: function argument
"""
g(x::Float64)::Float64 = x^2 / (sqrt(x^2 + one(Float64)) + one(Float64))

for i::Int in 1:20
    x::Float64 = 8.0^(-i)
    println("f(8^-$i) = $(f(x))")
    println("g(8^-$i) = $(g(x))")
end