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  • if <img alt="f(x)=\begin{Bmatrix} x^2-2x+2& 0\leq x <2 \\ 2x-6& 2\leq x\leq4 \\ 0& \text{otherwise} \end{Bmatrix}" src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%

if f(x)=\begin{Bmatrix} x^2-2x+2& 0\leq x <2 \\ 2x-6& 2\leq x\leq4 \\ 0& \text{otherwise} \end{Bmatrix}, then find the range of f(x)

Option: 1

[-2,4]


Option: 2

[-2,6]


Option: 3

[0,4]


Option: 4

[0,6]


Answers (1)

best_answer

\\f(x)=\begin{Bmatrix} x^2-4x+4& 0\leq x <2 \\ 2x-4& 2\leq x\leq4 \\ 0& otherwise \end{Bmatrix}\\\\For\,\, 0\leq x<2: \\ f(x)= x^2-4x+4\\ f('x)=2x-4\Rightarrow \text{critical point }x=2 \text{ and f'(x) is negative for x less than 2}\\ f''(x)=2>0\Rightarrow \text{minima at 2}\\ f(2)=0\\ f(0)=4\\\\ For\,\,2\leq x\leq 4 \\ f(x)=2x-4\rightarrow \text{monotonic increasing }\\ f(2)=0\\ f(4)=4\\ \text{After plotting the graph, we can see that the range of f(x) is }[0,4]

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Divya Prakash Singh

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