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If the range of the function \[f(x)=\frac{ x }{ 4 }\] is {28, 30, 32, 34, 36}, what is its domain?

A{112, 120, 128, 136, 144}

B{118, 122, 124, 132, 145}

C{110, 118, 122, 124, 137}

D{111, 124, 128, 132, 146}

Verified Answer :

The answer is A. 112,120,128,136,144
Given the function f(x)=x4f(x)=x4, substitute the range values into f(x)f(x) and solve for xx.

Substituting 28 into f(x)f(x):
28xx=x4=28⋅4=11228=x4x=28⋅4x=112

Substituting 30 into f(x)f(x):
30xx=x4=30⋅4=12030=x4x=30⋅4x=120

Substituting 32 into f(x)f(x):
32xx=x4=32⋅4=12832=x4x=32⋅4x=128

Substituting 34 into f(x)f(x):
34xx=x4=34⋅4=13634=x4x=34⋅4x=136

Substituting 36 into f(x)f(x):
36xx=x4=36⋅4=14436=x4x=36⋅4x=144

The domain of the given function then is {112,120,128,136,144}

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