#!/usr/bin/env julia

# Jacek Poziemski 272389

"""
    f(x::Float64)

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

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

"""
    g(x::Float64)

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

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

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