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Mail Tucker, Ge xLimiting Reactanlc Wait for Next Q Xb Login | bartlebyBb MyLab Math - R XWA4.dviwH 4 Ways to TakeO Not securemath.wsu.edu/math/faculty/remaley/220fa19WA4.pdfGWA4.dvi2/2[4] 3. Define f R- R by f(x)= rx d, where r and d are real constants. Show that for f to be linear, itis required that d 0. (the definition of a linear transformation is given in text section 1.8)+1:26 PMaType here to search9/18/2019X...

Question
Mail Tucker, Ge x
Limiting Reactan
lc Wait for Next Q X
b Login | bartleby
Bb MyLab Math - R X
WA4.dvi
wH 4 Ways to Take
O Not secure
math.wsu.edu/math/faculty/remaley/220fa19WA4.pdf
G
WA4.dvi
2/2
[4] 3. Define f R- R by f(x)
= rx d, where r and d are real constants. Show that for f to be linear, it
is required that d 0. (the definition of a linear transformation is given in text section 1.8)
+
1:26 PM
a
Type here to search
9/18/2019
X
...
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Mail Tucker, Ge x Limiting Reactan lc Wait for Next Q X b Login | bartleby Bb MyLab Math - R X WA4.dvi wH 4 Ways to Take O Not secure math.wsu.edu/math/faculty/remaley/220fa19WA4.pdf G WA4.dvi 2/2 [4] 3. Define f R- R by f(x) = rx d, where r and d are real constants. Show that for f to be linear, it is required that d 0. (the definition of a linear transformation is given in text section 1.8) + 1:26 PM a Type here to search 9/18/2019 X ...

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Step 1

Consider the linear function.

f(x) x +d
where r and d are real
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f(x) x +d where r and d are real

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Step 2

Since, a function

f RR is a linear transformation,
when f (px+ypf (x)+f(y)Vx,ye R and pe R is scalar
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f RR is a linear transformation, when f (px+ypf (x)+f(y)Vx,ye R and pe R is scalar

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Step 3

Therefore...

f(px+ y)r(px+y)+ d
f(px+y) p(rx)ry d
pf (x)+f(y)p(+d)+pyd
pf (x)+f(y)p()+ pd+ py+d
pf (x)+f(y) p(x)+ py +(p+1)d
pf (x)+y) p(rx+ y)+(p+1)d
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f(px+ y)r(px+y)+ d f(px+y) p(rx)ry d pf (x)+f(y)p(+d)+pyd pf (x)+f(y)p()+ pd+ py+d pf (x)+f(y) p(x)+ py +(p+1)d pf (x)+y) p(rx+ y)+(p+1)d

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