Question

Given T(x)={(x+5 if x<3),(-x+4 if x>3):} Evaluate the function P(x) at the values x=0,3,6

Answer 1

For the given piecewise function T(x)={(x+5 if x<3),(-x+4 if x≥3)}, the evaluation of the function P(x) at the values x=0, 3, 6 yields P(0)=5, P(3)=1, P(6)=−2.

Step-by-step explanation:

The piecewise function T(x) is defined differently for two intervals: for x<3, it is x+5, and for x≥3, it is −x+4. To find P(x), we evaluate T(x) at the specified values of x.

For x=0 (where x<3), P(0)=0+5=5.

For x=3 (where x≥3), P(3)=−(3)+4=1.

For x=6 (where x≥3), P(6)=−(6)+4=−2.

These results are obtained by substituting the given values into the appropriate expressions for T(x) based on the intervals defined in the piecewise function.

Note: The brackets in the function definition were unclear, so I assumed that the definition for x≥3 is −x+4. If this is not the case, the answer might need adjustment.