The function f:\mathbb{R}\to\mathbb{R} defined by,f(x)=3x^2+5, for all x∊\mathbb{R}, is

Correct Answer is : neither one-one nor onto

AP ICET 2016 Paper

Question : 122 of 200

Marks: +1, -0

The function

f : ℝ \to ℝ

defined by,

f(x)=3x^2+5

, for all

x∊ℝ

, is

Solution:

Given f : R → R,

f(x)=3x^2+5

for all x ∈ R
We can see that

f(x)=f(-x)

⇒ f (x) is not one-one function.
For all x ∈ R, the range of

3x^2+5

is [5, ∞] and this is a subset of R.
⇒ f (x) is not onto.
∴ f (x) is neither one-one nor onto.

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