Let $g\left( x \right) = 1 + x - \left[ x \right]$ and $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} { - 1,\;\;\;\;\;\;\;\;\;\;x 0\;\;\;} \end{array}} \right.\;{\rm{then}}\;{\rm{\;for}}$ for $x,f\left[ {g\left( x \right)} \right]$ is equal to

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

Let

g\left( x \right) = 1 + x - \left[ x \right]

and

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\begin{array}{cccccccccccccccccccc} { - 1,\;\;\;\;\;\;\;\;\;\;x < 0\;\;\;\;\;\;}\\ {0,\;\;\;\;\;\;\;\;\;\;\;\;\;x = 0,\;} \end{array}}\\ {1\;\;\;\;\;\;\;\;\;\;\;\;x > 0\;\;\;} \end{array}} \right.\;\mathrm{then}\;\mathrm{\;for}

for

x,f\left[ {g\left( x \right)} \right]

is equal to

View answer and explanation

Correct option: B

1

Option B (1) is correct because g(x) is always greater than 1, and f(x) is 1 for any input greater than 0.