Functions Quiz

Which of the following graphs represent a one to one function?

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 $f^{-1}$  An inverse function exists if _______________

• there exists a horizontal line that cuts the graph of f at most once.

• every vertical line x = k cuts the graph of f at most once.

• if  $\frac{1}{f\left(x\right)}$  is well defined.

• f is one to one function.

Given $f\left(x\right)=x^2+2x\ ,\ \ x\ <-1\$ , find the equation of  $f^{-1}\left(x\right)$ . 

•  $f^{-1}\left(x\right)=-\sqrt{x+1}-1$  

•  $f^{-1}\left(x\right)=\sqrt{x+1}-1$  

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

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

The range of a function, f is equivalent to _______

• $D_f$

• the values of y between the minimum and maximum points.

• $R_{f^{-1}}$

• $D_{f^{-1}}$

For the composite function fg to exist, ______________ .

• $D_g\subseteq R_f$

• $R_f\subseteq D_g$

• $R_g\subseteq D_f$

• $D_f\subseteq R_g$

Given $f\left(x\right)=\ln x$  and  $g\left(x\right)=x^2+2$  . Find the equation of fg(x).

•  $\ln\left(x^2+2\right)$  

•  $\left[\ln\left(x\right)\right]^2+2$  

•  $\left[\ln x\right]\left[x^2+2\right]$  

•  $\left[\ln\left(x^2\right)\right]+2$  

 $D_{gh}$  = ____________

•  $D_h$  

•  $D_g$  

•  $R_h$  

•  $R_g$  

Given  $g\left(x\right)=x^2+2,\ x>0$  and  $f\left(x\right)=ax+1,\ x\ >\ 0$ . Find  $R_{gf}$ .  

•  $\left(1,\infty\right)$  

•  $\left(3,\infty\right)$  

•  $\left(2a+1,\infty\right)$  

•  $\left(-\infty,1+2a\right)$  

Given $f\left(x\right)=3\left[\sin x\right]^3-4,\ -\frac{\pi}{3}<x<\frac{\pi}{2}$  , find  $R_{f^{-1}f}$ . 

•  $\left(-4,3\right)$  

•  $\left(-7,-1\right)$  

•  $\left(\frac{9}{4}\sqrt{\frac{3}{2}}-4,-1\right)$  

•  $\left(-\frac{\pi}{3},\frac{\pi}{2}\right)$  

A piecewise function f is defined as above. Find f(43).

 

• 0

• 1848

• 5

• 131