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Byju's Answer
Standard XIII
Mathematics
Using Graph to Find Range of a Function
If fx=maxx3,x...
Question

If f(x)=max(x3,x2,164) ∀ x∈[0,∞), then

A
f(x)=⎧⎪ ⎪⎨⎪ ⎪⎩x2, 0≤x≤1 x3, x>1
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B
f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩164, 0≤x≤14 x2, 14<x≤1 x3, x>1
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C
f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩164, 0≤x≤18 x2, 18<x≤1 x3, x>1
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D
f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩164, 0≤x≤18 x3, x>18
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Solution

The correct option is C f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩164, 0≤x≤18 x2, 18<x≤1 x3, x>1

Clearly, from the graph f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩164, 0≤x≤18 x2, 18<x≤1 x3, x>1

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