Let f : R → R be a function defined by f(x) = , then f is:

Question

Let f : R &#8594; R be a function defined by f(x) = , then f is:

Accepted Answer

One One / Many One
f(x) = , Domain x ∧ R
f′(x) =
f′(x) = > 0 ⇒ x ∈ (- ∞, 0) ∪
f′(x) < 0 ⇒ x ∈
f′(x) = 0 ⇒ x = 0,

Function is increasing and decreasing in different intervals, so non monotonic
∴ Many one function.
Onto / Into
f(x) =
2x² - x + 5 > 0, ∀ x ∈ R and 7x² + 2x + 10 > 0 ∀ x ∈ R
∵ a = 2 > 0 and ∵ a = 7 and D = 4 - 280 < 0
D = 1 - 40 = - 39 < 0
∴ f(x) > 0 ∀ x ∈ R
Also f(x) never tends to ± ∞as 7x² + 2x + 10 has no real roots, Range ≠ Codomain so into function.

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