A function f :
Question:

A function f : R → R is defined by f(x) = x2. Determine

(a) range of f,

(b) {x : f(x) = 4},

(c) [y : f(y) = −1].

Solution:

(a) Given:

(x) = x2     

Range of f = R+     (Set of all real numbers greater than or equal to zero)

(b) Given:

(x) = x2   

⇒ x2 = 4

⇒ x = ± 2

∴ {x : f (x) = 4 } = {  2, 2}.

(c) { y : f (y) = 1}

⇒ f (y) = 1   

It is clear that $x^{2}=-1$ but $x^{2} \geq 0$.

$\Rightarrow f(y) \neq-1$

 

$\therefore\{y: f(y)=-1\}=\Phi$

 

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