contestada

For exponential functions of the form f(x)=a^x, which of the following expressions is equal to f(r) • f(s)?
Answers :
A. f(r•s)
B. f(r^s)
C. f(r+s)

Respuesta :

konrad509

[tex]f(r)\cdot f(s)=a^r \cdot a^s=a^{r+s}=f(r+ s)[/tex]

The expression that is equal to f(r) • f(s) is f(r+s).

What is an Exponent?

  • It is a mathematical operator with the base and an exponent part.
  • It contains constant and variable.
  • It is governed by some laws, which is derived by the arithmetic operations.

Given: Function

f(x) = aˣ

∴ f(r) = [tex]a^{r}[/tex]

and

⇒ f(s) = [tex]a^{s}[/tex]

Now, the product of f(r) and f(s) is:

⇒ f(r) • f(s) = [tex]a^{r} . a^{s}[/tex]

Now, the law of product of exponent is, if the base of the two exponent is same then when the base is multiplied, the exponent will add.

[tex]A^{y}.A^{z} =A^{y+z}[/tex]

⇒ f(r) • f(s) = [tex]a^{r +s}[/tex]

Now, we will check the options.

Option (A): f(r•s)

⇒ f(r•s) = [tex]a^{rs}[/tex]

   ⇒ f(r•s) ≠ f(r) • f(s)

Hence, this option is incorrect.

Option (B): f([tex]r^{s}[/tex])

⇒ f([tex]r^{s}[/tex]) = [tex]a^{r^{s} }[/tex]

⇒ f([tex]r^{s}[/tex]) ≠ f(r) • f(s)

Hence, this option is incorrect.

Option (C): f(r+s)

⇒ f(r+s) =    [tex]a^{r+s}[/tex]

⇒ f(r+s) = f(r) • f(s)

Hence, this option is correct.

Therefore, For the given function the expression that is equal to f(r) • f(s) is f(r+s).

Learn more about the Exponent here: https://brainly.com/question/13585256

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