Questions: For the function (f(x)=2^2 x-1) calculate the following function values: (f(3)=) (f(4)=)

Transcript text: For the function $f(x)=2^{2 x-1}$ calculate the following function values: \[ \begin{array}{l} f(3)= \\ f(4)= \end{array} \]

Solution

Step 1: Identify the Base and Shift

The base of the exponential function is given as $a = 2$ and the horizontal shift is $b = 0.5$.

Step 2: Substitute and Simplify

For a given value of $x = 3$, we substitute it into the function to get $f(x) = 2^{x-0.5} = 2^{2.5}$.

Step 3: Calculate Function Values

Using the simplified expression, the value of the function is $f(x) = 5.657$ when rounded to 5 decimal places.

The value of the function $f(x) = 2^{x-0.5}$ for $x = 3$ is approximately 5.657.

Step 1: Identify the Base and Shift

The base of the exponential function is given as $a = 2$ and the horizontal shift is $b = 0.5$.

Step 2: Substitute and Simplify

For a given value of $x = 4$, we substitute it into the function to get $f(x) = 2^{x-0.5} = 2^{3.5}$.

Step 3: Calculate Function Values

Using the simplified expression, the value of the function is $f(x) = 11.314$ when rounded to 5 decimal places.

Final Answer:

The value of the function $f(x) = 2^{x-0.5}$ for $x = 4$ is approximately 11.314.

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