Math

QuestionFind the value of f(4)f(-4) for the function f(x)=3x2x+2f(x)=3 x^{2}-x+2.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=3xx+f(x)=3 x^{}-x+ . We are asked to find the value of the function when x=4x=-4, i.e., f(4)f(-4)

STEP 2

To find f(4)f(-4), we need to substitute x=4x=-4 into the function.
f(4)=(4)2(4)+2f(-4) =(-4)^{2} - (-4) +2

STEP 3

First, calculate the square of -.
()2=16(-)^{2} =16

STEP 4

Substitute (4)2(-4)^{2} with 1616 into the function.
f(4)=3(16)(4)+2f(-4) =3(16) - (-4) +2

STEP 5

Next, calculate the product of 33 and 1616.
3(16)=483(16) =48

STEP 6

Substitute 3(16)3(16) with 4848 into the function.
f(4)=48(4)+2f(-4) =48 - (-4) +2

STEP 7

Next, subtract 4-4 from 4848. Remember that subtracting a negative number is the same as adding a positive number.
48(4)=5248 - (-4) =52

STEP 8

Substitute 48(4)48 - (-4) with 5252 into the function.
f(4)=52+2f(-4) =52 +2

STEP 9

Finally, add 22 to 5252.
52+2=5452 +2 =54

STEP 10

Substitute 52+252 +2 with 5454 into the function.
f(4)=54f(-4) =54So, f(4)=54f(-4) =54.

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