Math

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 parts - f(x)=3x+f(x) =3x + for x<0x <0 - f(x)=3x+5f(x) =3x +5 for x0x \geq0
. We need to find the function values for x=1x = -1, x=0x =0, and x=x =.

STEP 2

First, let's find the function value for x=1x = -1. Since 1-1 is less than 00, we use the first part of the piecewise function.
f(1)=(1)+2f(-1) =(-1) +2

STEP 3

Calculate the value of f(1)f(-1).
f(1)=3(1)+2=3+2=1f(-1) =3(-1) +2 = -3 +2 = -1

STEP 4

Next, let's find the function value for x=0x =0. Since 00 is not less than 00, we use the second part of the piecewise function.
f(0)=3(0)+f(0) =3(0) +

STEP 5

Calculate the value of f(0)f(0).
f(0)=3(0)+5=0+5=5f(0) =3(0) +5 =0 +5 =5

STEP 6

Finally, let's find the function value for x=2x =2. Since 22 is not less than 00, we use the second part of the piecewise function.
f(2)=3(2)+5f(2) =3(2) +5

STEP 7

Calculate the value of f(2)f(2).
f(2)=3(2)+5=6+5=11f(2) =3(2) +5 =6 +5 =11So, the function values are f(1)=1f(-1) = -1, f(0)=5f(0) =5, and f(2)=11f(2) =11.

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