Let f(x)={x+1,x>02−x,x≤0 and g(x)={x+3,x<1,x2−2x−2,1≤x<2x−5,x≥2 Find the LHL and RHL of g(f(x)) at x=0 and, hence, fin x→0limg(f(x)).

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Question

Let $f (x) = {x + 1, x > 02 - x, x \leq 0$ and $g (x) = {x + 3, x < 1, x^{2} - 2 x - 2, 1 \leq x < 2 x - 5, x \geq 2$ Find the LHL and RHL of $g (f (x))$ at $x = 0$ and, hence, fin $x \to 0 lim g (f (x)) .$

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Scarlett Discussed

Let

f (x) = {x + 1, x > 02 - x, x \leq 0

and

g (x) = {x + 3, x < 1, x^{2} - 2 x - 2, 1 \leq x < 2 x - 5, x \geq 2

Find the LHL and RHL of

g (f (x))

x = 0

and, hence, fin

x \to 0 lim g (f (x)) .

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Question Text

Let

f (x) = {x + 1, x > 02 - x, x \leq 0

and

g (x) = {x + 3, x < 1, x^{2} - 2 x - 2, 1 \leq x < 2 x - 5, x \geq 2

Find the LHL and RHL of

g (f (x))

x = 0

and, hence, fin

x \to 0 lim g (f (x)) .