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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 :

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[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

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