Question

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?

Answer 1

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

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 $f(x) = a^{x}$, by algebra we have the following property:

$f(x + h) = a^{x+h} = a^{x}\cdot a^{h}$ (1)

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

$f(x+h) = a^{x}\cdot a^{h} = f(x) \cdot f(h)$ (2)

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

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