Let f - g - - be defined by f x - 2x - 1 andg x - x2 - 2- - x - respectively- Then- find a o f

Given: f, g:ℝ→ℝ defined by f ( x )=2x + 1 and g(x)=x^2 2 ∀ x ϵ ℝ Then composition function g ( f ( x ) ) nbsp; is read as ”g of f of x ” or gof (x) ∴ F ...

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Byju's Answer

Standard X

Mathematics

Discriminant

Let f , g : ℝ...

Question

Let f , g : $R \to R$ be defined
by $f (x) = (2 x + 1$ ) and
$g (x) = x^{2} - 2, \forall x ϵ R,$
respectively. Then, find a o f

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Solution

Given: $f, g : R \to R$ defined by
$f (x) = 2 x + 1 a n d g (x) = x^{2} - 2 \forall x ϵ R$

Then composition function g $(f (x))$ is read as $^{''} g of f of x '' or gof (x)$

$∴$ From given experssions of f (x) and g(x) gof
= $g (f (x))$
= ${(f (x))}^{2} - 2$
= ${(2 x + 1)}^{2} - 2$
= $4 x^{2} + 4 x - 1$

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