If f(x) = 1/2 (2^x 2^x) , then f(x + y). f(x – y) =
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Answer:hello bro, here your answer
Step-by-step explanation:Given that f(x)=
2
2
x
+2
−x
=
2
2
x
+
2
x
1
=
2
x+1
2
2x
+1
∴f(x+y)=
2
x+y+1
2
2(x+y)
+1
=
2
1
[2
x+y
+2
−(x+y)
]
Similarly, f(x−y)=
2
1
[2
x−y
+2
−(x−y)
]
∴f(x+y).f(x−y)=
2
1
[2
x+y
+2
−x−y
].
2
1
[2
x−y
+2
−x+y
]
=
4
1
(2
2x
+2
2y
+2
−2y
+2
−2x
)
=
4
1
[(2
2x
+2
2y
)+(2
−2y
+2
−2x
)]
=
4
1
[2f(2x)+2f(2y)]
=
2
1
[f(2x)+f(2y)]
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