The range of the function f(x) = ^ (7-x) P_ (x-3) is

Step-by-step solution

For f(x) = ^ (7-x) P_ (x-3) to be defined, the following conditions must be satisfied: 7 - x 0 x 7 x - 3 0 x 3 7 - x x - 3 2x 10 x 5 Also, x must be an integer. From the above inequalities, the possible values of x are 3, 4, 5 . Substituting these values into the function: For x = 3 , f(3) = ⁴P₀ = 1 For x = 4 , f(4) = ³P₁ = 3 For x = 5 , f(5) = ²P₂ = 2 Therefore, the range of the function is 1, 2, 3 . Answer: 1, 2, 3