Let g (x) = {\\begin{array}{ccc}−x & & x \leq 1 \ x + 1 & & x \geq 1 \\\end{array}. and f (x) = {\\begin{array}{ccc}1−x & & x \leq 0 \ x^{2\end{array}, , x > 0 ; }.. Consider the composition of f and g, i.e. (fog)(x) = f(g(x)). The number of discontinuities in (fog)(x) present in the interval (-∞, 0) is:

GATE Electrical Engineering (EE) 2017 Shift 2 Solved Paper

Question : 36 of 65

Marks: +1, -0

Let

g (x) = {\{\table −x, , x ≤ 1 ; x + 1, , x ≥ 1 ; }.

and

f (x) = {\{\table 1−x, , x ≤ 0 ; x^{2}, , x > 0 ; }.

.
Consider the composition of f and g, i.e. (fog)(x) = f(g(x)). The number of discontinuities in (fog)(x) present in the interval (-∞, 0) is:

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