Find the value of m such that g ( x ) = 2 x - 4 x + m is a self-inverse function.

Given g ( x ) = 2 x - 4 x + m is a self-inverse function. We know that, a function g is self-inverse if it has the property that g ( g ( x ) ) = x , for every x in the domain of g . In other words, g ( x ) = g - 1 x . Now, g g x = x ⇒ g 2 x - 4 x + m = x ⇒ 2 2 x - 4 x + m - 4 2 x - 4 x + m + m = x ⇒ 4 x - 8 x + m - 4 x + m x + m 2 x - 4 x + m + m x + m x + m = x ⇒ - 4 m - 8 2 x - 4 + x m + m 2 = x ⇒ - 4 m - 8 = x 2 x - 4 + x m + m 2 ⇒ - 4 m - 8 = 2 x 2 - 4 x + x 2 m + m 2 ⇒ - 4 m - 8 = ( 2 + m ) x 2 - 4 x + m 2 ⇒ 0 = 2 + m Therefore, the value of m = - 2 .

Find the value of m such that g ( x ) = 2 x - 4 x + m is a self-inverse function.

Given g ( x ) = 2 x - 4 x + m is a self-inverse function. We know that, a function g is self-inverse if it has the property that g ( g ( x ) ) = x , for every x in the domain of g . In other words, g ( x ) = g - 1 x . Now, g g x = x ⇒ g 2 x - 4 x + m = x ⇒ 2 2 x - 4 x + m - 4 2 x - 4 x + m + m = x ⇒ 4 x - 8 x + m - 4 x + m x + m 2 x - 4 x + m + m x + m x + m = x ⇒ - 4 m - 8 2 x - 4 + x m + m 2 = x ⇒ - 4 m - 8 = x 2 x - 4 + x m + m 2 ⇒ - 4 m - 8 = 2 x 2 - 4 x + x 2 m + m 2 ⇒ - 4 m - 8 = ( 2 + m ) x 2 - 4 x + m 2 ⇒ 0 = 2 + m Therefore, the value of m = - 2 .

State the domain and range for the function below: x - 5 - 1 0 1 4 9 y - 8 0 6 - 1 9 1

Given function is x - 5 - 1 0 1 4 9 y - 8 0 6 - 1 9 1 We know that a function is a relationship between the x and y values, where each x - value or input has only one y -value or output. And, the set of all x - values or inputs that have an output of real y -values is called domain of the function. Whereas The set of all the y - values or outputs of a function is called the range of the function. Thus, domain and range for the given function are as follows: Domain: - 5 , - 1 , 0 , 1 , 4 , 9 Range: - 8 , 0 , 6 , - 1 , 9 , 1