Let fx be defined on -2-2- and is given by fx- -1- -2- x- 0 x-1- 0 - x - 2- and gx-f-x - -fx- then find g-1

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

Let fx be d...

Question

Let $f (x)$ be defined on $[- 2, 2],$ and is given by $f (x) = {\begin{matrix} - 1, & - 2 \leq x \leq 0 x - 1, & 0 \leq x \leq 2 \end{matrix},$ and $g (x) = f (| x |) + | f (x) |,$ then find $g (- 1)$

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Solution

$g (- 1)$

$= f (| - 1 |) | + | f (- 1) |$
$= f (1) + | f (- 1) |$

$= (1 - 1) + | - 1 |$

$= 1$

Thus, The correct answer is 1.

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Let f(x) be defined on [−2,2], and is given by f(x)={−1,−2≤x≤0x−1,0≤x≤2, and g(x)=f(|x|)+|f(x)|, then find g(−1)

g(−1)=f(|−1|)|+|f(−1)|=f(1)+|f(−1)|=(1−1)+|−1|=1Thus, The correct answer is 1.

Let $f (x)$ be defined on $[- 2, 2],$ and is given by $f (x) = {\begin{matrix} - 1, & - 2 \leq x \leq 0 x - 1, & 0 \leq x \leq 2 \end{matrix},$ and $g (x) = f (| x |) + | f (x) |,$ then find $g (- 1)$

$g (- 1)$

$= f (| - 1 |) | + | f (- 1) |$
$= f (1) + | f (- 1) |$

$= (1 - 1) + | - 1 |$

$= 1$

Thus, The correct answer is 1.