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X
- WE WANT TO DETERMINE THE FOUR FUNCTION VALUES
USING THE PROVIDED TABLES.
NOTICE HOW THIS TABLE GIVES US THE X VALUES
AND THE FUNCTION VALUES FOR FUNCTION F.
REMEMBER WE CAN ALSO THINK OF THE X VALUES AS THE INPUTS
AND THE FUNCTION VALUES OR Y VALUES AS THE OUTPUTS.
AND THE SECOND TABLE DOES THE SAME BUT FOR FUNCTION G.
SO WE'RE FIRST GIVEN F + (G OF 2)
WHICH USING OUR DEFINITIONS HERE ON THE RIGHT
IS EQUIVALENT TO (F OF 2) + (G OF 2).
SO TO DETERMINE THE VALUE OF (F OF 2)
WE WANT TO FIND THE FUNCTION VALUE OR OUTPUT
WHEN THE INPUT OR THE X VALUE IS +2.
SO WE CAN SAY F OF THE INPUT IS EQUAL TO THE OUTPUT.
SO AGAIN IN BOTH CASES, THE X VALUES WOULD BE THE INPUTS
AND THE Y VALUES OR FUNCTION VALUES WOULD BE THE OUTPUTS.
SO FOR (F OF 2) NOTICE OUR FUNCTION F
WHEN THE X VALUE OR INPUT IS +2 THE OUTPUT IS -1.
SO (F OF 2) = -1.
AND THEN FOR FUNCTION G,
NOTICE WHEN THE INPUT OR X VALUE IS +2
THE OUTPUT OR FUNCTION VALUE IS 11.
SO WE HAVE -1 + 11 WHICH IS EQUAL TO 10.
FOR F - (G OF -3)
THIS WOULD BE EQUIVALENT TO (F OF -3) - (G OF -3).
GOING BACK TO THE TABLE FOR F
NOTICE WHEN THE X VALUE OR INPUT IS -3
THE OUTPUT OR FUNCTION VALUE IS +4.
SO WE'D HAVE +4 MINUS.
AND THEN FOR (G OF -3),
NOTICE WHEN THE INPUT OR X VALUE IS -3 FOR G,
THE FUNCTION VALUE OR OUTPUT IS +6.
SO (F OF -3) - (G OF -3) = 4 - 6 WHICH IS EQUAL TO -2.
NEXT WE HAVE X x G OF 1,
WHICH IS EQUIVALENT TO (F OF 1) x (G OF 1).
SO FOR F OF 1, NOTICE THAT FOR FUNCTION F
WHEN THE INPUT IS +1, THE OUTPUT OR FUNCTION VALUE IS -4.
SO HERE WE HAVE -4 x (4G OF 1).
NOTICE WHEN THE INPUT IS 1 THE FUNCTION VALUE OR OUTPUT IS +6.
SO (F OF 1) x (G OF 1) = -4 x 6 WHICH IS EQUAL TO -24.
AND THEN FINALLY WE HAVE F DIVIDED BY (G OF -1)
WHICH IS EQUIVALENT TO (F OF -1) DIVIDED BY (G OF -1).
FOR (F OF -1)
NOTICE THAT WHEN THE INPUT OR X VALUE IS -1 FOR FUNCTION F,
THE OUTPUT IS -4.
SO HERE WE HAVE -4 DIVIDED BY.
FOR (G OF -1) NOTICE THAT FOR G WHEN THE INPUT IS -1
THE OUTPUT IS +2.
SO (F OF -1) DIVIDED BY (G OF -1)
IS EQUAL TO -4 DIVIDED BY 2 WHICH IS EQUAL TO -2.
I HOPE YOU FOUND THIS EXPLANATION HELPFUL.