Consider the two functions defined on :

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the two functions defined on R\mathbb{R}: (i) g(x)=∣x∣g(x)=|x| (ii) h(x)=xh(x)=x Which one of the following statements about their ranges is correct? (a) g(R)=[0,∞),  h(R)=[0,∞)g(\mathbb{R})=[0,\infty),\; h(\mathbb{R})=[0,\infty) (b) g(R)=R,  h(R)=[0,∞)g(\mathbb{R})=\mathbb{R},\; h(\mathbb{R})=[0,\infty) (c) g(R)=[0,∞),  h(R)=Rg(\mathbb{R})=[0,\infty),\; h(\mathbb{R})=\mathbb{R} (d) g(R)=(0,∞),  h(R)=Rg(\mathbb{R})=(0,\infty),\; h(\mathbb{R})=\mathbb{R}

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