Let f,g: R → R be two functions defined as f(x) = |x| + x and g(x) = | x | - x ∀ x ∈ R. Then (fog) (x) for x

Question

Let f,g: R → R be two functions defined as f(x) = |x| + x and g(x) = | x | - x ∀ x ∈ R. Then (fog) (x) for x < 0 is (A) 0 (B) 4x (C) -4x (D) 2x

Tardigrade Admin · Accepted Answer

f ( x )=| x |+ x = begincases2 x text if x ≥ 0 0 text if x <0 endcases and g ( x )=| x |- x = begincases0 text if x ≥ 0 -2 x text if x < 0 endcases Now for x < 0,( f ° g )( x )= f [ g ( x )] = f [-2 x ]=2(-2 x )=-4 x

Q. Let $f, g : R \to R$ be two functions defined as $f (x) = ∣ x ∣ + x$ and $g (x) = ∣ x ∣ - x \forall x \in R$ . Then $(f o g) (x)$ for $x < 0$ is

0

4x

-4x

2x

$f (x) = ∣ x ∣ + x = {2 x 0 if x \geq 0 if x < 0$ and $g (x) = ∣ x ∣ - x = {0 - 2 x if x \geq 0 if x < 0$
Now for $x < 0, (f \circ g) (x) = f [g (x)]$
$= f [- 2 x] = 2 (- 2 x) = - 4 x$

Q. Let f,g:R→R be two functions defined as f(x)=∣x∣+x and g(x)=∣x∣−x∀x∈R. Then (fog)(x) for x<0 is

0

4x

-4x

2x

f(x)=∣x∣+x={2x0​ if x≥0 if x<0​ and g(x)=∣x∣−x={0−2x​ if x≥0 if x<0​ Now for x<0,(f∘g)(x)=f[g(x)] =f[−2x]=2(−2x)=−4x

Q. Let $f, g : R \to R$ be two functions defined as $f (x) = ∣ x ∣ + x$ and $g (x) = ∣ x ∣ - x \forall x \in R$ . Then $(f o g) (x)$ for $x < 0$ is

$f (x) = ∣ x ∣ + x = {2 x 0 if x \geq 0 if x < 0$ and $g (x) = ∣ x ∣ - x = {0 - 2 x if x \geq 0 if x < 0$
Now for $x < 0, (f \circ g) (x) = f [g (x)]$
$= f [- 2 x] = 2 (- 2 x) = - 4 x$