Week 3 Assignment

Solve for the value of x. Round to the nearest thousandths.  $8^x-3\ =\ 36$  

Solve for x. Round to nearest thousandths. $\log_x81=4$  

 $\left(x^4+x^2-14x\ -48\right)\ \div\left(x-3\right)$  

•  $x^3+3x^2+10x+16$  

•  $x^3-3x^2+10x+16$  

•  $x^3+3x^2+10x-16$  

•  $x^3-3x^2-8x+16$  

Find the inverse of:  $f\left(x\right)=6^x$  

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

•  $f^{-1}\left(x\right)=\log_6\left(x\right)$  

•  $f^{-1}\left(x\right)=\log_x^{ }\left(6\right)$  

•  $f^{-1}\left(x\right)=\sqrt{6^x}$  

Find the inverse of:  $f\left(x\right)=2\left(x-1\right)^2+8$  

•  $f^{-1}\left(x\right)=\sqrt{\frac{x-8}{2}}+1$  

•  $f^{-1}\left(x\right)=\frac{1}{2}\left(x+1\right)^2-8$  

•  $f^{-1}\left(x\right)=\frac{1}{2}\sqrt{x+1}-8$  

•  $f^{-1}\left(x\right)=\sqrt{\frac{x}{2}-8}+1$  

Write an exponential equation that goes through the following points: (-2, 8) and (2, 0.5)

Write your answer in the following format: y = a(b)^x

Write an exponential equation that goes through the following points: (-1, 15) and (2, 0.12)

Write your answer in the following format: y = a(b)^x

Write an exponential equation that goes through the following points: (2, 3.703) and (6, 103.63)

• $y=0.7\left(2.3\right)^x$

• $y=0.02\left(2.46\right)^x$

• $y=0.6\left(0.2\right)^x$

• $y=3\left(2.46\right)^x$

Write the equation for a polynomial with roots at x = 2, x = -4, a double root at x = 3 and goes through the point (5, 10)

• $y=\frac{5}{54}\left(x-2\right)\left(x+4\right)\left(x-3\right)^2$

• $y=\frac{5}{224}\left(x+2\right)\left(x-4\right)\left(x+3\right)^2$

• $y=\frac{5}{864}\left(x-2\right)\left(x+4\right)\left(x+3\right)^2$

• $y=\frac{10}{54}\left(x-2\right)\left(x+4\right)\left(x-3\right)^2$

Write an equation in standard form of polynomial equation with roots -4 + 9i and -4 - 9i.

(Write your answer in following form: y = x^2 + bx + c)