Question

Evaluate the function rule for the given value. f(x) = 3^x for x = –5

Answer 1

For this case we have the following function:

`f (x) = 3 ^ x`

We must evaluate the function for
`x = -5`

So, we have:

`f (-5) = 3 ^ {-5}`

By definition of power properties it is fulfilled that:

`a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}`

Thus:

`f (-5) = \frac {1} {3 ^ 5} = \frac {1} {3 * 3 * 3 * 3 * 3} = \frac {1} {243}`

Answer:

`\frac {1} {243}`

Answer 2

f(-5) = 1/ 243

Explanation:

f(x) = 3^x

Let x=-5

f(-5) = 3^-5

Since the exponent is negative, it will move to the denominator

f(-5) = 1/3^5

f(-5) = 1/ 243