Let f- be the function defined by fx-sin -3x-2 - x - R- Then f is invertible-

Check if function is bijective Given: f:ℝ→ℝ ⇒ nbsp; Co domain of (f)=ℝ f(x)=sin (3x+2) Now –1≤sin⁡(3x+2)≤ 1 [(∵ −1≤sinθ≤ 1 ∀ nbsp; θ ϵ ℝ)] ⇒ nbsp;−1≤ f ...

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Standard XII

Mathematics

Quadratic Formula for Finding Roots

Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be the function defined by $f (x) = sin (3 x + 2) \forall x ϵ R$ . Then $f$ is invertible.

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Solution

Check if function is bijective

Given: $f : R \to R$
$\Rightarrow$ Co-domain of $(f) = R$
$f (x) = sin (3 x + 2)$
Now $- 1 \leq sin (3 x + 2) \leq 1$
$[(∵ - 1 \leq sin θ \leq 1 \forall θ ϵ R)]$
$\Rightarrow - 1 \leq f (x) \leq 1$
$\Rightarrow$ Range of $(f) = [- 1, 1] \neq$ Co-domain of $(f)$
$∴ f (x)$ is not onto function
$\Rightarrow f$ is not invertible.

Hence, the given statement is false.

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Quadratic Formula for Finding Roots

Standard XII Mathematics

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Let f:R→R be the function defined by f(x)=sin(3x+2) ∀ x ϵ R. Then f is invertible.

Check if function is bijective Given: f:R→R ⇒ Co-domain of (f)=R f(x)=sin(3x+2) Now –1≤sin(3x+2)≤1 [(∵−1≤sinθ≤1 ∀ θ ϵ R)] ⇒−1≤f(x)≤1 ⇒ Range of (f)=[–1,1]≠ Co-domain of (f) ∴f(x) is not onto function ⇒f is not invertible. Hence, the given statement is false.

Let $f : R \to R$ be the function defined by $f (x) = sin (3 x + 2) \forall x ϵ R$ . Then $f$ is invertible.