Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Suppose f is a function which follows this pattern, where x and h are any numbers: f(a + h) = f(a)*f(h) Which type of function is f?

Sagot :

xero099

[tex]f[/tex] has to be a power function in order to satisfy the recurrence pattern [tex]f(x + h) = f(x) \cdot f(h)[/tex]

Procedure - Determination of a function with a pattern.

In this case, we must assume a given function and check such assumption fulfill the given recurrence. Let suppose that [tex]f(x) = a^{x}[/tex], by algebra we have the following property:

[tex]f(x + h) = a^{x+h} = a^{x}\cdot a^{h}[/tex] (1)

And by the definition given in statement, we have the following conclusion:

[tex]f(x+h) = a^{x}\cdot a^{h} = f(x) \cdot f(h)[/tex] (2)

Therefore, [tex]f[/tex] has to be a power function in order to satisfy the recurrence pattern [tex]f(x + h) = f(x) \cdot f(h)[/tex]. [tex]\blacksquare[/tex]

To learn more on power functions, we kindly invite to check this verified question: https://brainly.com/question/5168688

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.