Domain of a function Quiz 1

Question 1

Try to find out the domain 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

Not defined $$\le {{\sin }^{-1}}\left( 2x+5 \right)\le {{\sin }^{-1}}\left( 7 \right)$$

Answer

$${{\sin }^{-1}}\left( 3 \right)\le {{\sin }^{-1}}\left( 2x+5 \right)\le$$ Not defined

Answer

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

Question 2

If the function $$f\left( x \right)={{\log }_{4}}\left( -{{\log }_{\frac{1}{2}}}\left( 1+\dfrac{1}{{{x}^{\frac{1}{6}}}} \right)-1 \right)$$ is given to us. Then what will be its domain.

Accepted Answer

(0,1)

Answer

(0,1]

Answer

[0,1]

Answer

[0,1)

Question 3

If $$f\left( x \right)=a{{x}^{2}}+bx+c$$ and $$g\left( x \right)=3$$, then domain of $$g\circ f(x)$$ is:

Accepted Answer

3

Answer

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

Answer

$$\left[ 0,\infty  \right)$$

Answer

$$\dfrac{3}{a+b}$$

Question 4

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

Accepted Answer

Real number

Answer

Rational number

Answer

Integers

Answer

Natural number

Question 5

Consider the function in the form of $$f\left( x \right)=\sqrt{1-7x}$$ and $$g\left( x \right)=x+3$$. Try to find the domain of $$f\circ g(x)$$.

Accepted Answer

$$x\in \left[ -\dfrac{20}{7},\infty  \right)$$

Answer

$$x\in \left[ -7,\infty  \right)$$

Answer

$$\left( -\infty ,\dfrac{-1}{7} \right]$$

Answer

$$\left( -\infty ,-7 \right]$$