The graph of real-valued functions $f (x)$ is the following. The function is

f (x) = x - | x |

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f (x) = x + | x |

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f (x) = 2 x

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None of these

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Solution

The correct option is A $f (x) = x + | x |$
Let $f (x) = x + ∣ x ∣$
When $x \leq 0, ∣ x ∣= - x ⟹ f (x) = x - x = 0$
When $x > 0, ∣ x ∣= x ⟹ f (x) = x + x = 2 x$
From the graph $y = 0, x \leq 0$ and $y = 2 x, x > 0$
$⟹ y = x + ∣ x ∣$

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The graph of real-valued functions f(x) is the following. The function is

The correct option is A f(x)=x+|x|Let f(x)=x+∣x ∣When x≤0,∣x ∣=−x⟹f(x)=x−x=0When x>0,∣x ∣=x⟹f(x)=x+x=2xFrom the graph y=0,x≤0 and y=2x,x>0⟹y=x+∣x ∣

The graph of real-valued functions $f (x)$ is the following. The function is

The correct option is A $f (x) = x + | x |$
Let $f (x) = x + ∣ x ∣$
When $x \leq 0, ∣ x ∣= - x ⟹ f (x) = x - x = 0$
When $x > 0, ∣ x ∣= x ⟹ f (x) = x + x = 2 x$
From the graph $y = 0, x \leq 0$ and $y = 2 x, x > 0$
$⟹ y = x + ∣ x ∣$