Functions — Quiz 3

Questions in this quiz (10)

1. Let $$f(x)$$ have an inverse function $$h(x)$$. Then $$h(f(x))=$$?

   • $$0$$
   • $$1$$
   • $$x$$
   • $$f(x)\cdot h(x)$$

2. The function $$f(x)=x^3+2x-4$$ has exactly one real zero. It is between:

   • $$0$$ and $$1$$
   • $$1$$ and $$2$$
   • $$2$$ and $$3$$
   • $$3$$ and $$4$$

3. The range of $$y=\ln(2+\sin x)$$ is:

   • $$(-\Infty,\ln(3)]$$
   • $$[0,\ln(3)]$$
   • $$[-1,1]$$
   • $$(-1,1)$$

4. Solve for $$b$$: $$\log_b(b^4)=8$$

   • $$-1$$
   • $$0$$
   • $$1$$
   • No real solution

5. Let $$f^{-1}$$ be the inverse function of $$f(x)=x^3-5$$. Then $$f^{-1}(x)=$$?

   • $$\frac{1}{x^3+5}$$
   • $$(x+5)^3$$
   • $$\sqrt[3]{x+5}$$
   • $$\frac{1}{(x+5)^3}$$

6. The set of $$x$$-intercepts of the graph of $$f(x)=x^3-x^2-4x+4$$ is:

   • $$\{-2,2\}$$
   • $$\{-1,1,4\}$$
   • $$\{-2,1,2\}$$
   • $$\{-4,-1,1\}$$

7. If the domain of $$f$$ is restricted to the open interval $$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$$, then the range of $$f(x)=e^{2\tan x}$$ is:

   • the set of all real numbers
   • the set of positive real numbers
   • the set of nonnegative real numbers
   • the set of real numbers in the interval (0,1]

8. Which of the following represents a reflection of the graph of $$y=f(x)$$ in the $$y$$-axis?

   • $$y=-f(x)$$
   • $$y=f(-x)$$
   • $$y=f(|x|)$$
   • $$y=-f(-x)$$

9. The smallest positive $$x$$ for which the function $$f(x)=\cos\left(\frac{x}{4}\right)+2$$ is a maximum is:

   • $$2\pi$$
   • $$4\pi$$
   • $$6\pi$$
   • $$8\pi$$

10. Evaluate: $$\sin(\arccos(\frac{1}{2}))$$

    • $$-\frac{\sqrt{3}}{2}$$
    • $$\frac{\sqrt{3}}{2}$$
    • $$-\frac{1}{2}$$
    • $$\frac{1}{2}$$