Range of a function Quiz 1

Question 1

The range of the function $$f\left( x \right)={{x}^{2}}+9$$, where $$x\in \left( 3,9 \right)$$ is:

Accepted Answer

(18, 90)

Answer

[18, 90]

Answer

[18, 90)

Answer

(18, 90]

Question 2

Try to find out the range of the function $$f\left( x \right)={{\sin }^{-1}}\left( 2x+5 \right)$$ for $$\forall x\in \left[ -2,3 \right]$$.

Accepted Answer

None of the above

Answer

$$	ext{not defined}\le {{\sin }^{-1}}\left( 2x+5 ight)\le {{\sin }^{-1}}\left( 7 ight)$$

Answer

$${{\sin }^{-1}}\left( 3 ight)\le {{\sin }^{-1}}\left( 2x+5 ight)\le 	ext{not defined}$$

Answer

$${{\sin }^{-1}}\left( 3 \right)\le {{\sin }^{-1}}\left( 2x+5 \right)\le {{\sin }^{-1}}\left( 7 \right)$$

Question 3

The range of the function $$f\left( x ight)=	an \left( {{x}^{2}}+1 ight)$$ is:

Accepted Answer

$$\left( -\infty ,\infty  \right)$$

Answer

$$[-1,1]$$

Answer

$$(-1,1)$$

Answer

$$(0,1)$$

Question 4

The range of $$f\left( x \right)={{\left( \dfrac{1}{1-x} \right)}^{\frac{1}{2}}}$$ is

Accepted Answer

$$\left( -\infty ,1 \right)$$

Answer

$$\left( -\infty ,1 \right]$$

Answer

$$\left( -\infty ,0 \right)$$

Answer

$$\left( -\infty ,0 \right]$$

Question 5

Solve $$f\left( x \right)=\cos \left( x+\dfrac{\pi }{2} \right)-\sin x$$ such that its range is,

Accepted Answer

[-2,2]

Answer

[0,2]

Answer

(-2,2)

Answer

(0,2)