Let f(x)=|x| and g(x)=[x], (where, [.] denotes the greatest integer function). Then, (f o g)' (- 1) is

Question

Let f(x)=|x| and g(x)=[x], (where, [.] denotes the greatest integer function). Then, (f o g)' (- 1) is (A) 0 (B) does not exist (C) -1 (D) 1

Tardigrade Admin · Accepted Answer

(f o g)(x)=f(g(x))=f([x])=|[x]| Now, LHL of (f o g) prime(-1)= lim h arrow 0+ (( text fog )(-1-h)-( text fog )(-1)/-h) = lim h arrow 0+ (|[-1-h]|- mid[-||1/-h) = lim h arrow 0+ (|-2|-|-1|/-h)= lim h arrow 0+ (1/-h) arrow-∞ ∴ (f o g) prime(-1) does not exist.

Q. Let $f (x) = ∣ x ∣$ and $g (x) = [x],$ (where, $[.]$ denotes the greatest integer function). Then, $(f o g)^{^{'}} (- 1)$ is

$0$

does not exist

$- 1$

$1$

Q. Let f(x)=∣x∣ and g(x)=[x], (where, [.] denotes the greatest integer function). Then, (fog)′(−1) is

0

does not exist

−1

1

(fog)(x)=f(g(x))=f([x])=∣[x]∣ Now, LHL of (fog)′(−1)=limh→0+​−h( fog )(−1−h)−( fog )(−1)​ =limh→0+​−h∣[−1−h]∣−∣[−∣∣1​ =limh→0+​−h∣−2∣−∣−1∣​=limh→0+​−h1​→−∞ ∴(fog)′(−1) does not exist.

Q. Let $f (x) = ∣ x ∣$ and $g (x) = [x],$ (where, $[.]$ denotes the greatest integer function). Then, $(f o g)^{^{'}} (- 1)$ is

$0$

$- 1$

$1$