Which of the following functions is not onto

Question

Which of the following functions is not onto (A) f: R arrow R , f(x)=3 x+4 (B) f: R arrow R +, f(x)=x2+2 (C) f: R + arrow R +, f(x)=√x (D) none of these

Tardigrade Admin · Accepted Answer

The function f(x)=3 x+4 is onto as for y ∈ R , f((y-4/3))=y. The function f: R + arrow R +, f(x)=√x is onto as for y ∈ R +, f(y2)=y ⋅ f: R arrow R +, f(x)=x2+2 is not onto as 1 ∈ R +has no pre-image.

Q. Which of the following functions is not onto

$f : R \to R, f (x) = 3 x + 4$

$f : R \to R^{+}, f (x) = x^{2} + 2$

$f : R^{+} \to R^{+}, f (x) = x$

none of these

The function $f (x) = 3 x + 4$ is onto as for $y \in$ $R, f (\frac{y - 4}{3}) = y$ .
The function $f : R^{+} \to R^{+}, f (x) = x$ is onto as for $y \in R^{+}, f (y^{2}) = y \cdot f : R \to R^{+}, f (x) = x^{2} + 2$ is not onto as $1 \in R^{+}$ has no pre-image.

Q. Which of the following functions is not onto

f:R→R,f(x)=3x+4

f:R→R+,f(x)=x2+2

f:R+→R+,f(x)=x​

none of these

The function f(x)=3x+4 is onto as for y∈ R,f(3y−4​)=y. The function f:R+→R+,f(x)=x​ is onto as for y∈R+,f(y2)=y⋅f:R→R+,f(x)=x2+2 is not onto as 1∈R+has no pre-image.

$f : R \to R, f (x) = 3 x + 4$

$f : R \to R^{+}, f (x) = x^{2} + 2$

$f : R^{+} \to R^{+}, f (x) = x$

The function $f (x) = 3 x + 4$ is onto as for $y \in$ $R, f (\frac{y - 4}{3}) = y$ .
The function $f : R^{+} \to R^{+}, f (x) = x$ is onto as for $y \in R^{+}, f (y^{2}) = y \cdot f : R \to R^{+}, f (x) = x^{2} + 2$ is not onto as $1 \in R^{+}$ has no pre-image.