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Question

Consider the rational function f(x)=x34x2+15x8x22. Then

A
domain of f is R{2}
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B
there are three pre-images of 4
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C
there is only one pre-image of 4
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D
domain of f is R{±2}
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Solution

The correct option is D domain of f is R{±2}
f is meaningful if
x220
i.e., x±2
Domain of f is R{±2}.

We have to find the pre-image of 4
i.e., we have to find those values in the domain of f for which f(x)=4
x34x2+15x8x22=4
x34x2+15x8=4x28
x38x2+15x=0
x(x28x+15)=0
x(x3)(x5)=0
x=0,3,5

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