Functions — Quiz 1

Questions in this quiz (10)

1. Find the domain of $$g(x)=\frac{\sqrt{7-x}}{x-2}.$$

   • $$(-7,2)\cup(2,\infty)$$
   • $$(-2,7)\cup(7,\infty)$$
   • $$(-\infty,2)\cup(2,7]$$
   • $$[-2,7)\cup(7,\infty)$$

2. If $$f(x)=x^2+6x-7$$ and $$g(x)=x-3$$, then find $$\frac{f(x)}{g(x)}$$.

   • $$\frac{20}{x-3}$$
   • $$x+9+\frac{20}{x-3}$$
   • $$7+\frac{3}{x-3}$$
   • $$\frac{6x-7}{x-3}$$

3. If $$f(x)=3x^2+2$$ and $$g(x)=\sqrt{x+1}$$, find $$f(g(x))$$.

   • $$x+2$$
   • $$x+3$$
   • $$2x+3$$
   • $$3x+5$$

4. Find the inverse of the one-to-one function $$g(x)=\sqrt[3]{x+5}$$.

   • $$g^{-1}(x)=\frac{1}{3}x^3+5$$
   • $$g^{-1}(x)=x+5$$
   • $$g^{-1}(x)=x^3-5$$
   • $$g^{-1}(x)=(x+5)^3$$

5. Find the zeros of $$g(x)=x^4-5x^2$$.

   • $$-5$$, $$5$$
   • $$0$$, $$-\sqrt{5}$$, $$\sqrt{5}$$
   • $$-\sqrt{5}$$, $$\sqrt{5}$$
   • $$0$$, $$5$$

6. Consider the function:$$g(x)=\frac{2}{a}\sin(ax)$$For what value of $$a$$ does $$g$$ have a period of $$\pi$$?

   • $$-2$$
   • $$0$$
   • $$1$$
   • $$2\pi$$

7. Consider the function $$g(x)=\frac{2}{a}\sin(ax).$$ What is the amplitude of $$g$$?

   • $$a$$
   • $$\pi.a$$
   • $$2\pi.a$$
   • $$\frac{2}{|a|}$$

8. Consider the function $$g(x)=2+\cos\left(\frac{\pi x}{4}\right).$$ What is the smallest positive value of $$x$$ for which $$g$$ is a minimum?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

9. The domain of $$h(x)=\frac{\sqrt{x-5}}{x^2-9}$$ is:

   • $$x\neq\pm3$$
   • $$x\le5$$ and $$x\neq\pm3$$
   • $$x\ge5$$ and $$x\neq\pm3$$
   • $$x>5$$

10. If $$f(x)=2x^3-5x+7$$ and $$g(x)=4,$$ then $$g(f(x))=$$?

    • $$8x^3-20x+28$$
    • $$4x^3-5x+7$$
    • $$2x^3-5x+7$$
    • $$4$$