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QuestionGiven the function r(x)=−23x+4r(x)=-\frac{2}{3} x+4, find:
1. r(−6)r(-6)
2. r(12)r\left(\frac{1}{2}\right)
3. Solve for xx when r(x)=−4r(x)=-4.

Studdy Solution

STEP 1

Assumptions1. The function is given as r(x)=−3x+4r(x)=-\frac{}{3} x+4 . We need to find the values of r(−6)r(-6), r(1)r\left(\frac{1}{}\right) and the value of xx for which r(x)=−4r(x)=-4

STEP 2

To find the value of r(−6)r(-6), we substitute x=−6x=-6 in the given function.
r(−6)=−2(−6)+4r(-6)=-\frac{2}{}(-6)+4

STEP 3

implify the expression to find the value of r(−6)r(-6).
r(−6)=+=8r(-6)=+=8

STEP 4

To find the value of r(12)r\left(\frac{1}{2}\right), we substitute x=12x=\frac{1}{2} in the given function.
r(12)=−23(12)+4r\left(\frac{1}{2}\right)=-\frac{2}{3}\left(\frac{1}{2}\right)+4

STEP 5

implify the expression to find the value of r(12)r\left(\frac{1}{2}\right).
r(12)=−13+4=323r\left(\frac{1}{2}\right)=-\frac{1}{3}+4=3 \frac{2}{3}

STEP 6

To find the value of xx for which r(x)=−4r(x)=-4, we set r(x)=−4r(x)=-4 and solve for xx.
−23x+4=−4-\frac{2}{3}x+4=-4

STEP 7

Subtract4 from both sides of the equation to isolate the term with xx on one side.
−23x=−4−4-\frac{2}{3}x=-4-4

STEP 8

implify the right side of the equation.
−23x=−8-\frac{2}{3}x=-8

STEP 9

Multiply both sides of the equation by −32-\frac{3}{2} to solve for xx.
x=−8×−32x=-8 \times -\frac{3}{2}

STEP 10

implify the expression to find the value of xx.
x=12x=12So, the values are r(−6)=8r(-6)=8, r(2)=323r\left(\frac{}{2}\right)=3 \frac{2}{3}, and x=12x=12 when r(x)=−4r(x)=-4.

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