Question

Define the function formula for each of the following given the function definitions for f, g, and h .

f ( x ) = √ x + 5
g ( x ) = 3 x − 6
h ( x ) = 7/ x

Answer 1

The functions are given by f(x) = √x + 5 which involves taking the square root of x and adding 5, g(x) = 3x - 6 which involves multiplying x by 3 and subtracting 6, and h(x) = 7/x which involves dividing 7 by x.

Step-by-step explanation:

The question asks to define the function formula for three separate functions, where f(x) = \sqrt{x} + 5, g(x) = 3x - 6, and h(x) = \frac{7}{x}. These definitions provide the explicit formula for how to calculate the value of each function given any input x.

For function f, the formula indicates that you first take the square root of the input x, and then add 5 to the result. It is important to note that x must be a non-negative number since you cannot take the square root of a negative number in the realm of real numbers.

The function g simply multiplies the input by 3 and then subtracts 6 from the result, which can be done with any real number value of x. Lastly, the function h divides the number 7 by the input x, in which case x must not be zero because division by zero is undefined.