Question

Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.

Options

• f(x) − f(y)

• f(y)

• 2f(x) f(y)

• f(x) f(y)

Answer 1

Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to 2f(x) f(y).

Explanation:

Given, f(x) = `(a^x + a^(-x))/2 (a > 2)`

Then, f(x + y) + f (x − y)

put x + y → x

and x − y →x

= `(a^(x + y) + a^-(x + y))/2 + (a^(x - y) + a^-(x - y))/2`

= `(a^x (a^y + a^-y) + a^-x (a^y + a^-y))/2`

= `((a^x + a^-x)(a^y + a^-y))/2`

= `2.((a^x + a^-x))/2 . ((a^y + a^-y))/2`

= 2f(x) f(y)