For some constants a and b let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\]the function f has the property that f(f(x)) = x for all x. what is a + b?

The value of a+b is 4.

Step-by-step explanation:

The given function is

It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.

For x≤3,

For x>3,

At x=0,

Using property f(f(x))=x,

                    .... (1)

At x=1,

Using property f(f(x))=x,

                    .... (2)

Subtract equation (2) from equation (1).

Divide both sides by 2.

Substitute this value in equation (1).

The value of a is and value of b is . The value of a+b is

Therefore the value of a+b is 4.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

answer: what are the following choices