If f(x) = x, g(x) = 2x2 + 1 and h(x) = x+ 1 then (hogof)(x) =

Question

If f(x) = x, g(x) = 2x2 + 1 and h(x) = x+ 1 then (hogof)(x) =  (A) x2 + 2 (B) 2x2 + 2 (C) x2 + 1 (D) 2(x2 + 1)

Tardigrade Admin · Accepted Answer

Given f(x)=x, g(x)=2 x2+1 and h(x)=x+1 hogof (x) =h(g(f(x))) =h(g(x)) ldots ldots[∵ f(x)=x] =h(2 x 2+1) ldots[∵ g ( x )=2 x 2+1] =2 x 2+1+1 =2 x2+2 =2(x2+1) ∴ operatornamehogof( x )=2( x 2+1)

Q. If $f (x) = x, g (x) = 2 x^{2} + 1$ and $h (x) = x + 1$ then $(h o g o f) (x) =$

$x^{2} + 2$

$2 x^{2} + 2$

$x^{2} + 1$

$2 (x^{2} + 1)$

Given $f (x) = x, g (x) = 2 x^{2} + 1$ and $h (x) = x + 1$
hogof $(x)$
$= h (g (f (x)))$
$= h (g (x)) \dots\dots [∵ f (x) = x]$
$= h (2 x^{2} + 1) \dots [∵ g (x) = 2 x^{2} + 1]$
$= 2 x^{2} + 1 + 1$
$= 2 x^{2} + 2$
$= 2 (x^{2} + 1)$
$∴ hogof (x) = 2 (x^{2} + 1)$

Q. If f(x)=x,g(x)=2x2+1 and h(x)=x+1 then (hogof)(x)=

x2+2

2x2+2

x2+1

2(x2+1)