Question

Given the function f(x)={(3x^(2)-5,x<-1),(6x^(2)-9,-1<=x<=1),(7,x>1):} Calculate the following values:

Answer 1

To calculate values for the piecewise function, substitute the x values into the appropriate function expression based on the given intervals for x.

Step-by-step explanation:

The student asked to calculate the following values for the piecewise function f(x):

• For x < -1, use f(x) = 3x2 - 5.
• For -1 ≤ x ≤ 1, use f(x) = 6x2 - 9.
• For x > 1, use f(x) = 7.

To calculate specific values, you substitute the x values into the correct function based on the given ranges.

1. If x is less than -1, for example, x = -2, calculate f(-2) by plugging -2 into 3x2 - 5 to get 3(-2)2 - 5, which is 3(4) - 5 = 12 - 5 = 7.
2. If x falls between -1 and 1, including both -1 and 1, for example, x = 0, calculate f(0) by plugging 0 into 6x2 - 9 to get -9.
3. If x is greater than 1, for example, x = 2, f(2) is simply 7 as per the last piece of the function.