Functions — Quiz 7

Questions in this quiz (8)

1. Which of these is all the real numbers NOT in the domain of $$f(x)=\frac{1}{|3x-4|}?$$

   • $${-\frac{4}{3}}$$
   • $${\frac{4}{3},-\frac{4}{3}}$$
   • $${-\frac{4}{3},1}$$
   • $${\frac{4}{3}}$$

2. If $$g(x)=\frac{x-2}{(x-3)(x+5)}$$, what are all the real numbers NOT in the domain of $$g(x+1)$$?

   • $$2 , -6$$
   • $$1 , -5$$
   • $$3 , -5$$
   • $$4 ,-6$$

3. For $$f(x)=(x+a)(x+b)$$ with integers $$a,b$$, it is given that $$f(-25)$$ > $$0$$, $$f(-18)$$ < $$0$$, and $$f(-10)$$ > $$0$$. Find one possible value of $$a$$.

   • $$12$$
   • $$20$$
   • $$10$$
   • $$5$$

4. If $$ f(g(x))=x^2-x-2$$ and $$f(x)=x^2-3x$$, then find $$g(x)$$.

   • $$g(x)=x^2-1$$
   • $$g(x)=2x-1$$
   • $$g(x)=x+1$$
   • $$g(x)=x-4$$

5. Find the inverse of the function when $$x$$<$$4$$:$$f(x)=|x-4|+2$$

   • $$f^{-1}(x)=x-4$$
   • $$f^{-1}(x)=\frac{2}{x-4}$$
   • $$f^{-1}(x)=-x+4$$
   • $$f^{-1}(x)=-x+6$$

6. What is the x-coordinate of the extreme point of the function $$f(x) = 5x^2 - 20x + 9$$?

   • 2
   • 5
   • -5
   • 220

7. A linear function $$g$$ has a slope of $$2$$. In addition, $$g^{-1}(1)=5$$. Find the value of $$g(6)$$.

   • $$12$$
   • $$3$$
   • $$5$$
   • $$-9$$

8. Find the inverse of the function $$f(x)=5e^{2x+1}+3$$

   • $$f^{-1}(x)=\left(\ln\left(\frac{x+3}{5}\right)+1\right)$$
   • $$f^{-1}(x)=\frac{1}{2}\left(\ln\left(\frac{x}{5}\right)+1\right)$$
   • $$f^{-1}(x)=\frac{1}{2}\left(\ln\left(\frac{x-3}{5}\right)-1\right)$$
   • $$f^{-1}(x)=\left(\ln\left(\frac{x+3}{5}\right)-1\right)$$