Let the functions f, g, h are defined from the set of real numbers R to R such that f(x)=x2-1, g(x)=√(x2+1) and h(x)= beginmatrix 0,if x le 0 x,if x ge 0 endmatrix . , then ho(fog)(x) is defined by

Question

Let the functions f, g, h are defined from the set of real numbers R to R such that f(x)=x2-1, g(x)=√(x2+1) and h(x)= beginmatrix 0,if x le 0 x,if x ge 0 endmatrix . , then ho(fog)(x) is defined by (A)  x  (B)  x2  (C)  0  (D) None of these

Tardigrade Admin · Accepted Answer

Given that, f(x)=x2-1, g(x)=√(x2+1) and h(x)= beginmatrix 0,if x<0 x,if x ge 0 endmatrix . ∴ ho(fog)(x)=hof g(x) =hof √(x2+1) =h (√x2+1)2-1 =h x2+1-1 =h x2 =x2

Q. Let the functions $f, g, h$ are defined from the set of real numbers $R$ to $R$ such that $f (x) = x^{2} - 1, g (x) = (x^{2} + 1)$ and $h (x) = {0, i f x, i f x \leq 0 x \geq 0$ , then $h o (f o g) (x)$ is defined by

$x$

$x^{2}$

$0$

None of these

Given that, $f (x) = x^{2} - 1, g (x) = (x^{2} + 1)$ and $h (x) = {0, i f x, i f x < 0 x \geq 0$
$∴$ $h o (f o g) (x) = h o f {g (x)}$
$= h o f {(x^{2} + 1)}$
$= h {(x^{2} + 1)^{2} - 1}$
$= h {x^{2} + 1 - 1}$
$= h {x^{2}}$
$= x^{2}$

Q. Let the functions f,g,h are defined from the set of real numbers R to R such that f(x)=x2−1,g(x)=(x2+1)​ and h(x)={0,ifx,if​x≤0x≥0​ , then ho(fog)(x) is defined by

x

x2

0

None of these

Given that, f(x)=x2−1,g(x)=(x2+1)​ and h(x)={0,ifx,if​x<0x≥0​ ∴ ho(fog)(x)=hof{g(x)} =hof{(x2+1)​} =h{(x2+1​)2−1} =h{x2+1−1} =h{x2} =x2

Q. Let the functions $f, g, h$ are defined from the set of real numbers $R$ to $R$ such that $f (x) = x^{2} - 1, g (x) = (x^{2} + 1)$ and $h (x) = {0, i f x, i f x \leq 0 x \geq 0$ , then $h o (f o g) (x)$ is defined by

$x$

$x^{2}$

$0$

Given that, $f (x) = x^{2} - 1, g (x) = (x^{2} + 1)$ and $h (x) = {0, i f x, i f x < 0 x \geq 0$
$∴$ $h o (f o g) (x) = h o f {g (x)}$
$= h o f {(x^{2} + 1)}$
$= h {(x^{2} + 1)^{2} - 1}$
$= h {x^{2} + 1 - 1}$
$= h {x^{2}}$
$= x^{2}$