Study Guide (Algebra 2)

What operation allows us to verify if functions are inverses?

Select the two expressions which are inverses of each other:

Select the two expressions which are inverses of each other:

 $Given\ f\left(x\right)\ =\ 3x\ +\ 2\ and\ g\left(x\right)\ =\ 2x\ +\ 4,\ find\ f\left(x\right)\ \cdot\ g\left(x\right)$ 

 $Given\ f\left(x\right)\ =\ 9\ -\ 3x\ and\ g\left(x\right)\ =\ 5x\ -\ 7,\ find\ f\ +\ g.$  

 $Given\ f\left(x\right)\ =\ x^2\ +\ 1\ and\ g\left(x\right)\ =\ 2x\ -\ 5,\ find\ f\left(x\right)\ -\ g\left(x\right).$ 

 $f\left(n\right)\ =\ 2n\ +1\ and\ g\left(n\right)\ =\ 3n,\ find\ f\ +\ g.$  

 $Given\ f\left(x\right)\ =\ x^2\ +\ 9\ and\ g\left(x\right)\ =\ x\ -\ 9,\ find\ \left(f\ -\ g\right)\left(x\right).$ 

 $g\left(x\right)=\sqrt{x}$   $f\left(x\right)=2x+1$  
Find  $\left(f+g\right)\left(9\right)$  

 $f\left(x\right)=x^2\ \ \$   $g\left(x\right)=2x$  

Find  $\left(f\cdot g\right)\left(-3\right)$  

 $g\left(x\right)=4x+5$  

Divide and simplify (if possible):
 $f\left(x\right)=5x-1$ 
  $g\left(x\right)=x-7$  
 $\left(\frac{g}{f}\right)\left(x\right)$  

Divide and simplify (if possible):
 $f\left(x\right)=x^2-4$ 
  $g\left(x\right)=x^2+4x+4$  
 $\left(\frac{f}{g}\right)\left(x\right)$  

Divide and simplify (if possible):
 $f\left(x\right)=x^2-6x-16$ 
  $g\left(x\right)=x^2-4x-12$  
 $\frac{g\left(x\right)}{f\left(x\right)}$  

Let

 $f\left(x\right)=4x-3$  and  $g\left(x\right)=x^{2\ }-4$  .

Find  $f\left(g\left(3\right)\right).$  

Let

 $f\left(x\right)=4x-3$  and  $g\left(x\right)=x^{2\ }-4$  .

Find  $g\left(f\left(x\right)\right).$