MCQ
Given the function $f(x) = \frac{{{a^x} + {a^{ - x}}}}{2},\;(a > 2)$. Then $f(x + y) + f(x - y) = $
- ✓$2f(x).f(y)$
- B$f(x).f(y)$
- C$\frac{{f(x)}}{{f(y)}}$
- DNone of these
✓
Answer
Correct option: A.
$2f(x).f(y)$
a
(a) We have $f(x + y) + f(x - y)$
(a) We have $f(x + y) + f(x - y)$
$ = \frac{1}{2}\,\left[ {{a^{x + y}} + {a^{ - x - y}} + {a^{x - y}} + {a^{ - x + y}}} \right]$
$ = \frac{1}{2}\,\left[ {{a^x}({a^y} + {a^{ - y}}) + {a^{ - x}}({a^y} + {a^{ - y}})} \right]$
$ = \frac{1}{2}\,({a^x} + {a^{ - x}})\,\,({a^y} + {a^{ - y}}) = 2f(x)\,f(y)$.
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