Math, asked by Dineshkumar02032006, 6 hours ago

If f(x) = 1/2 (2^x 2^x) , then f(x + y). f(x – y) =

Answers

Answered by ckarunakumari
0

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)]

Similar questions