Let f- be the function defined by fx-2x-3 - x- Write f -1

Given :f ( x )=2x 3 ∀ x ϵℝ Let (f ( x )) be denoted by y ⇒ y=2x 3 ⇒ x=y+3/2 Now, Replace y by x amp; x by (f ^ 1)in above nbsp;equation. ⇒ nbsp;f^ ...

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Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 1

Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be the
function defined by
$f (x) = 2 x - 3 \forall x ϵ R$
Write $f^{- 1}$

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Solution

Given : $f (x) = 2 x - 3 \forall x ϵ R$

Let $(f (x))$ be denoted by y

$\Rightarrow y = 2 x - 3$

$\Rightarrow x = \frac{y + 3}{2}$

Now, Replace y by x & x by $(f^{- 1})$ in above equation.

$\Rightarrow f^{- 1} = \frac{x + 3}{2}$

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Integration of Irrational Algebraic Fractions - 1

Standard XII Mathematics

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Let f:R→R be the function defined by f(x)=2x−3 ∀ xϵR Write f−1

Given :f(x)=2x−3 ∀ xϵR Let (f(x)) be denoted by y ⇒y=2x−3 ⇒x=y+32 Now, Replace y by x & x by (f−1)in above equation. ⇒f−1=x+32

Let $f : R \to R$ be the
function defined by
$f (x) = 2 x - 3 \forall x ϵ R$
Write $f^{- 1}$

Given : $f (x) = 2 x - 3 \forall x ϵ R$

Let $(f (x))$ be denoted by y

$\Rightarrow y = 2 x - 3$

$\Rightarrow x = \frac{y + 3}{2}$

Now, Replace y by x & x by $(f^{- 1})$ in above equation.

$\Rightarrow f^{- 1} = \frac{x + 3}{2}$