Question

For the exponential function f(x)=3⁽¹⁻ˣ⁾, evaluate f(2.5).

Answer 1

To evaluate the function f(x) = 3^(1-x) at x = 2.5, substitute the value of x into the function. First simplify the exponent and then evaluate the exponential expression to get the final answer.

Step-by-step explanation:

To evaluate the function f(x) = 3^(1-x) at x = 2.5, we substitute the value of x into the function.

So, f(2.5) = 3^(1-2.5)

First, we simplify the exponent: 1-2.5 = -1.5

Now, we evaluate 3^(-1.5). Since the exponent is negative, we can rewrite it as 1/3^1.5

Next, we cube the digit term: 3^1.5 = (3^(1))^1.5 = 3^1.5 = 3^(3/2)

Finally, we convert the fractional exponent to a radical form: 3^(3/2) = sqrt(3^3) = sqrt(27) = 3sqrt(3)

Therefore, f(2.5) = 3sqrt(3).