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QuestionEvaluate the piecewise function f(x)f(x) for the following values: (a) f(−1)f(-1), (b) f(0)f(0), (c) f(2)f(2).

Studdy Solution

STEP 1

Assumptions1. The function is defined as a piecewise function, with two separate equations for when x is less than0 and when x is greater than or equal to0. . We are asked to find the function values for x = -1,0, and.

STEP 2

We will start by finding the function value for x = -1. Since -1 is less than0, we will use the equation for when x is less than0, which is x+2x +2.
f(−1)=(−1)+2f(-1) =(-1) +2

STEP 3

Calculate the function value for x = -1.
f(−1)=3(−1)+2=−3+2=−1f(-1) =3(-1) +2 = -3 +2 = -1

STEP 4

Next, we will find the function value for x =0. Since0 is not less than0, we will use the equation for when x is greater than or equal to0, which is 3x+3x +.
f(0)=3(0)+f(0) =3(0) +

STEP 5

Calculate the function value for x =0.
f(0)=3(0)+5=0+5=5f(0) =3(0) +5 =0 +5 =5

STEP 6

Finally, we will find the function value for x =2. Since2 is greater than0, we will use the equation for when x is greater than or equal to0, which is 3x+53x +5.
f(2)=3(2)+5f(2) =3(2) +5

STEP 7

Calculate the function value for x =2.
f(2)=3(2)+5=6+5=11f(2) =3(2) +5 =6 +5 =11So, the function values are(a) f(−1)=−1f(-1) = -1 (b) f(0)=5f(0) =5 (c) f(2)=11f(2) =11

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