Let a function be defined as f(x) = c^x + c^-x2, for c > 0. What is the value of f(x + y) + f(x - y) ?

Let a function be defined as f(x) = c^x + c^-… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

Let a function be defined as $f(x) = \frac{c^x + c^{-x}}{2}$ , for $c > 0$ . What is the value of $f(x + y) + f(x - y)$ ?

Correct answer marked below

2f(x) + 2f(y)

f(x) + f(y)

4f(x)f(y)

2f(x)f(y)

Correct

f(x)f(y)

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Explanation

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We compute:

f(x + y) + f(x - y) = \frac{c^{x+y} + c^{-x-y}}{2} + \frac{c^{x-y} + c^{y-x}}{2} = \frac{c^{x+y} + c^{-x-y} + c^{x-y} + c^{y-x}}{2}

.

We note the answer must combine the four terms

c^{\pm x \pm y}

and include the constant

\frac{1}{2}

.…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.