Question

If $f(x)=a^{x},$ show that $f(A+B)=f(A) \cdot f(B)$

   If $f(x)=a^{x},$ show that $f(A+B)=f(A) \cdot f(B)$

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 6, Problem 125

Instant Answer

Solved by Expert James Kiss

06/14/2020

Step 1

Step 1: First, we substitute $A+B$ into the function $f(x)$, which gives us $f(A+B) = a^{A+B}$. Show more…

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If $f(x)=a^{x},$ show that $f(A+B)=f(A) \cdot f(B)$

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Key Concepts

Exponential Function

An exponential function is a mathematical function of the form f(x) = a^x, where the base a is a constant and the variable x is the exponent. This function is fundamental in mathematics because it models situations where quantities grow or decay at rates proportional to their current value, and it exhibits properties that differentiate it from linear or polynomial functions.

Properties of Exponents

The properties of exponents include rules that govern how exponential expressions behave under operations like multiplication and addition of exponents. A key rule is that a^(x+y) = a^x * a^y, which illustrates how adding exponents corresponds to multiplying their exponential forms. This property is essential for understanding exponential functions and simplifying expressions that involve them.

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