Question

f(x)=$x^2$ for x < 2

g(x)= $x^2$ for x > -1

Range of f(x)= range of g(x)

• A. True
• B. False

Answer 1

The correct option is A

True

f(x)=$x^2$ for x < 2

Range of f(x): when x<2

$\Rightarrow$ -$\infty$< x < 2

$\Rightarrow$ x ∈ (-$\infty$,2) $\Rightarrow$ x ∈ (-$\infty$,0) U [0,2)

For x ∈ [0,2) $\Rightarrow$ $x^2$ ∈ [0,4) ------------(1)

For x ∈ (-$\infty$,0) $\Rightarrow$ $x^2$ ∈ (0,$\infty$)------------(2)

From (1) & (2), $x^2$ ∈ [0,$\infty$)

g(x)=$x^2$ for x > -1

Range of g(x): x > -1

$\Rightarrow$ -1< x < $\infty$

$\Rightarrow$ x ∈ (-1,$\infty$) $\Rightarrow$ x ∈ (-1,0) U [0,$\infty$)

For x ∈ (-1,0) , $x^2$ ∈ (0,1)

For x ∈ [0,$\infty$), $x^2$ ∈ [0,$\infty$)

Hence range of g(x) = [0,$\infty$)

So, Range of f(x) = Range of g(x)