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.

30

step-by-step explanation:

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