Question

Write the definition of a function that takes as input the three numbers. The function returns true if the first number to the power of the second number equals the third number; otherwise, it returns false. (Assume that the three numbers are of type double.)

Short answer

Define a function, use `pow(a, b)` to calculate the power, compare it with `c`, and return true or false based on the comparison.

Step-by-step solution

Defining the Function

First, define a function that takes three parameters. In this case, since the numbers are of type `double`, we'll name the function `checkPowerEquality` and the parameters `a`, `b`, and `c`. The function signature will look like this in a programming language: `bool checkPowerEquality(double a, double b, double c)`.

Implementing the Power Operation

Inside the function, calculate the result of raising the first number `a` to the power of the second number `b`. This can be accomplished using a power function, often available in libraries like `math.h` in C or `cmath` in C++. In our function, we would use `pow(a, b)` to compute this.

Comparing the Result

After calculating the power, compare it to the third number `c`. If `pow(a, b)` is equal to `c`, the function should return `true`.

Returning the Result

If `pow(a, b)` is not equal to `c`, then the function should return `false`. This comparison gives the final decision on whether the first number raised to the power of the second equals the third number.

Final Code Implementation

Here is what the complete function might look like: ```c++ bool checkPowerEquality(double a, double b, double c) { return pow(a, b) == c; } ``` This function uses the `pow` function to perform the power calculation and compares the result to `c`. The `==` operator checks if the values are equal, and the function returns `true` or `false` accordingly.

Key concepts

Understanding Power Operation

The power operation is a crucial mathematical concept that allows us to multiply a number by itself a given number of times. For example, if you have a base number "a" and an exponent "b", the power operation will result in the base number "a" being multiplied by itself "b" times. This can be written as \( a^b \).

In programming, most languages provide a simple way to perform power operations using functions from standard libraries. For instance, C++ offers the `pow` function in the `cmath` library. When you want to calculate the result of raising "a" to the power of "b", you simply call `pow(a, b)`. This abstraction makes implementing power operations straightforward and efficient.

• Base (a): The number to be multiplied by itself.
• Exponent (b): Indicates how many times to multiply the base by itself.

This operation is used frequently in mathematics, physics, and computer programming when dealing with exponential growth, scientific calculations, and algorithms that require repeated multiplication.

Parameter Passing Explained

Parameter passing is a method used in programming to provide inputs to functions. It allows you to pass values from your main program or another function to the function you're calling. This is a key concept because it determines how information flows through your program.

When you define a function, you specify parameters that it expects to receive. In our example, the function `checkPowerEquality` takes three parameters: `a`, `b`, and `c`, all of which are of type `double`. By declaring these parameters, you ensure that the function knows what inputs to expect to conduct its operations.

• Actual Parameters: The real values passed to the function, often referred to as arguments.
• Formal Parameters: The parameters defined in the function declaration or the function signature.

Using parameter passing, you can make functions reusable and adaptable, as they can work with different sets of values without needing to be modified. This flexibility is one of the hallmarks of effective function design and promotes code efficiency and clarity.

Return Statements in Functions

Return statements are fundamental in functions to deliver the result of a computation back to wherever the function was called. They end the function's execution and send a value back to the caller. In our example function `checkPowerEquality`, the return statement produces a `true` or `false` based on the comparison result.

Here's how it works in a step-by-step manner:

1. After executing the necessary calculations or condition checks within the function, you reach the return statement.
2. If the conditions met in the function result in a true comparison (in our case, if \( \text{pow}(a, b) == c \)), the function returns `true`.
3. If not, it returns `false`. This is made possible by the `==` operator in the statement, which evaluates whether the left and right expressions yield the same result.

The return statement is vital for any function meant to solve a problem and provide an outcome:

• It marks the end of the function's execution.
• Provides a means to send data back to the function's caller.

Without a return statement, your function would not be able to provide results back to the main program or other functions, making it impossible to utilize the computed data or decision outcomes.