Question
If $f(x) \geq 0$ for all $x,$ then $f(2-x)$ is(A) $\geq-2$(B) $\geq 0$(C) $\geq 2$(D) $\leq 0$(E) $\leq 2$
Step 1
This means that the range of the function $f(x)$ is all non-negative real numbers. Show more…
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If $f(x)=\left\{\begin{array}{l}2+x, x \geq 0 \\ 2-x, x<0\end{array}\right.$, then $f(f(x))$ is given by (a) $\mathrm{f}(\mathrm{f}(\mathrm{x}))=\left\{\begin{array}{l}4+\mathrm{x}, \mathrm{x} \geq 0 \\ 4-\mathrm{x}, \mathrm{x}<0\end{array}\right.$ (b) $\mathrm{f}(\mathrm{f}(\mathrm{x}))=\left\{\begin{array}{c}4+\mathrm{x}, \mathrm{x} \geq 0 \\ \mathrm{x}, \mathrm{x}<0\end{array}\right.$ (c) $f(f(x))=\left\{\begin{array}{c}4-x, x \geq 0 \\ x, x<0\end{array}\right.$ (d) $\mathrm{f}(\mathrm{f}(\mathrm{x}))=\left\{\begin{array}{l}4+2 \mathrm{x}, \mathrm{x} \geq 0 \\ 4-2 \mathrm{x}, \mathrm{x}<0\end{array}\right.$
$f(x)=\max \{2-x, 2+x, 4\} x \in R$ is (a) $f(x)=\mid \begin{array}{cc}2-x & x \geq 2 \\ 4 & -2<x<2 \\ 2+x & x \leq-2\end{array}$ (b) $f(x)=\mid \begin{array}{cc}2-x & -2<x<2 \\ 4 & x \geq 2 \\ 2+x & x \leq-2\end{array}$ (c) $f(x)=\mid \begin{array}{cc}2-x & x \leq-2 \\ 4 & x \geq 2 \\ 2+x & -2<x<2\end{array}$ (d) $f(x)=\mid \begin{array}{cc}2-x & x \leq-2 \\ 4 & -2<x<2 \\ 2+x & x \geq 2\end{array}$
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