declare @Date_received date = '2013-02-23';

select
    @Date_received,
    dateadd(dd, -1, dateadd(wk, datediff(wk, cast('1900-01-01' as date), @Date_received), cast('1900-01-01' as date)))

select
    @Date_received,
    DATEFROMPARTS(DatePart(yyyy,DATEADD(dd, (DATEPART(dw, @Date_received) - 1) * - 1, @Date_received)),
                  DatePart(mm,DATEADD(dd, (DATEPART(dw, @Date_received) - 1) * - 1, @Date_received)),
                  DatePart(dd,DATEADD(dd, (DATEPART(dw, @Date_received) - 1) * - 1, @Date_received)))

ALTER FUNCTION [dbo].[FctDateTime_FirstDayOfWeek]


(

	@Date date
)

RETURNS date
with schemabinding
AS
BEGIN
declare @firstDate date

declare @Daysdiff int = dateDiff(dd,cast('1900-01-01' as date),@Date)%7
select @firstDate = DATEADD(dd, @Daysdiff*-1, @Date)

	RETURN @firstDate 

END

Alter FUNCTION [dbo].[FctDateTime_FirstDayOfWeek2]


(
	-- Add the parameters for the function here
	@Date date
)

RETURNS date
with schemabinding
AS
BEGIN
declare @firstDate date

declare @Daysdiff int = dateDiff(dd,(datefromparts('1900','01','01')),@Date)%7  --- ***Correct line. Cast is not determenistic

select @firstDate = DATEADD(dd, @Daysdiff*-1, @Date)

	RETURN @firstDate 

END

Alter FUNCTION [dbo].[FctDateTime_FirstDayOfWeek2]


(
	-- Add the parameters for the function here
	@Date date
)

RETURNS date
with schemabinding
AS
BEGIN
declare @firstDate date

declare @Daysdiff int = dateDiff(dd,(CONVERT(datetime, '1900-01-01', 101)),@Date)%7 ---*** Changed line. Convert is determenistic. 

select @firstDate = DATEADD(dd, @Daysdiff*-1, @Date)

	RETURN @firstDate 

END