Solve this

Question:

Let $f: R \rightarrow R: f(x)=x^{2}$

Determine

(i) range (f)

(ii) $\{x: f(x)=4\}$

 

Solution:

Given: $f(x)=x^{2}$

The graph for the given function is

(i) Range(f):

For finding the range of the given function, let y = f(x)

Therefore,

$y=x^{2}$

$x=\sqrt{y}$

The value of $y \geq 0$.

Hence, Range(f) is $[0, \infty)$.

(ii) Let $y=f(x)=x^{2}$

Given $y=4$

Therefore, $x^{2}=4$

$x=2$ or $x=-2$

The set of values for which $y=4$ is $x=\{2,-2\}$.

 

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