The function f: R→ R defined by f(x) = 3 - 4x is

Question

The function f: R→ R defined by f(x) = 3 - 4x is (A) Onto (B) Not onto (C) Not one-one (D) None of these

Tardigrade Admin · Accepted Answer

Let y ∈ R be any real number, such that f(x) = y ∴ y = 3 - 4x ⇒ 4x=3-y ⇒ x=(3-y/4) So, for any real number y ∈ R, there exists (3-y/4) ∈ R such that f ((3-y/4))=3-4((3-y/4))=3-3+y=y Hence, f is onto.

Q. The function $f$ : $R \to R$ defined by $f (x) = 3 - 4 x$ is

Onto

Not onto

Not one-one

None of these

Let $y \in R$ be any real number, such that $f (x) = y$
$∴ y = 3 - 4 x$
$\Rightarrow 4 x = 3 - y$
$\Rightarrow x = \frac{3 - y}{4}$
So, for any real number $y \in R$ , there exists $\frac{3 - y}{4} \in R$ such that $f (\frac{3 - y}{4}) = 3 - 4 (\frac{3 - y}{4}) = 3 - 3 + y = y$
Hence, $f$ is onto.

Q. The function f : R→R defined by f(x)=3−4x is

Onto

Not onto

Not one-one

None of these

Let y∈R be any real number, such that f(x)=y ∴y=3−4x ⇒4x=3−y ⇒x=43−y​ So, for any real number y∈R, there exists 43−y​∈R such that f(43−y​)=3−4(43−y​)=3−3+y=y Hence, f is onto.

Q. The function $f$ : $R \to R$ defined by $f (x) = 3 - 4 x$ is