Find the Range of Functions

Solution

For

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

the square of every real number is always non-negative.

Therefore,

$$ f(x)\ge 0 $$

Hence, the range of \(f\) is:

$$ [0,\infty) $$

For

$$ g(x)=\sin x $$

we know that the value of \(\sin x\) always lies between \(-1\) and \(1\).

Therefore,

$$ -1\le \sin x\le 1 $$

Hence, the range of \(g\) is:

$$ [-1,1] $$

For

$$ h(x)=x^2+1 $$

since

$$ x^2\ge 0 $$

adding \(1\) gives

$$ x^2+1\ge 1 $$

Hence, the range of \(h\) is:

$$ [1,\infty) $$