If f - A - B defined as fx - x2-2x-1-1-x-12 is onto function- then set B is equal to

OR Show that the function $f : R \to R$ defined by $f (x) = \frac{x}{x^{2} + 1} \forall x ϵ R$ is neither one-one nor onto. Also, if $g : R \to R$ is defined as g(x) = 2x-1, find fog(x).

Q. If

A = {- 2, - 1, 0, 1, 2}

and

f : A

\to

B

is a surjection defined by

f (x) =

x^{2} + x + 1

, then find

B

Q. Let A = R – {2} and B = R – {1}. If f : A → B is a function defined by

f (x) = \frac{x - 1}{x - 2},

show that f is one-one and onto. Find f^–¹.

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If f:A→B defined as f(x)=x2+2x+11+(x+1)2 is onto function, then set B is equal to

The correct option is D (−∞,∞)f:A→B,f(x)=x2+2x+11+(x+1)2∵11+(x+1)2>0∴f(x)=x2+2x+11+(x+1)2a=1,b=2D=4−4×1×(1+ve)≥0∵xϵR

If $f : A \to B$ defined as $f (x) = x^{2} + 2 x + \frac{1}{1 + (x + 1)^{2}}$ is onto function, then set B is equal to

The correct option is D $(- \infty, \infty)$
$f : A \to B, f (x) = x^{2} + 2 x + \frac{1}{1 + {(x + 1)}^{2}} ∵ \frac{1}{1 + {(x + 1)}^{2}} > 0 ∴ f (x) = x^{2} + 2 x + \frac{1}{1 + {(x + 1)}^{2}} a = 1, b = 2 D = 4 - 4 \times 1 \times (\frac{1}{+ v e}) \geq 0 ∵ x ϵ R$