Algebra 2 Final 2021

1. Find (f + g)(x).  f(x) = x -2 and g(x) = 3x.

• 4x+5
  

• x+-2

• 4x-2

• 4x+2

2. Find (f ⋅ g)(x). f(x) = x -2 and g(x) = 3x

• $3x^2-6x$

• $3x^2+6x$

• $3x^2+6$

• 3x-6

3. Find the inverse of g(x) = 2x - 4.

• $g^{-1\left(x\right)}=x+4$

• $g^{-1}\left(x\right)=x+4$

• $g^{-1}\left(x\right)=2x+4$

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

 $4.Simplify\ (3+\sqrt{2})(2–\sqrt{2}).$  

•  $8+5\sqrt{2}$  

•  $4-\sqrt{2}$  

•  $4+\sqrt{2}$  

•  $8-\sqrt{2}$  

5 . Simplify  $\sqrt{180}+\sqrt{80}$  

•  $5\sqrt{2}$  

•  $8\sqrt{2}$  

•  $4\sqrt{2}$  

•  $\sqrt{260}$  

6. Write the expression  $5^{\frac{5}{4}}$   in radical form.

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• 
• 
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7. Solve $\sqrt{2x-4}=4$  

• -10

• 4

• 2

• 10

8. Which function represents exponential growth?

• $y=3\left(\frac{5}{3}\right)^x$

• $y=4x^2$

• $y=12\left(0.4\right)^x$

• $y=10\left(\frac{1}{2}\right)^x$

9. Solve $9^{\left(x+2\right)}=27^{\left(4x-3\right)}$  

• 13

•  $\frac{13}{10}$  

•  $\frac{10}{13}$  

• 10

 $x^3=27$  Write the equation in logarithmic form.

•  $\log_x27=3$  

•  $\log_327=x$  

•  $\log_{27}3=x$  

•  $\log_{27}x=3$