Assessment ((Real Life Problems Involving Inverse Function)

Which of the following is the inverse of

 $f\left(x\right)=\sqrt{\frac{x+3}{7}}?$  

•  $f^{-1}\left(x\right)=7x^2+3$  

•  $f^{-1}\left(x\right)=7x^2-3$  

•  $f^{-1}\left(x\right)=3x^2+7$  

•  $f^{-1}\left(x\right)=3x^2-7$  

Which of the following is the inverse of f(x) = 6x + 5 ?

• $f^{-1}\left(x\right)=\frac{x-5}{6}$

• $f^{-1}\left(x\right)=\frac{x+5}{6}$

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

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

A study found that the relationship between the number of hours (x) and the students exam's scores f(x) is given by the equation f(x) = 10x + 55. Using this information, what will be the estimated number of scores of the student he spent 4 hours in studying?

• 95

• 85

• 75

• 65

The relationship between temperatures in degree celcius and in degree Fahrenheit is given by $\degree C=\frac{5}{9}\left(\degree F-32\right).\$  What is the corresponding value in degree Fahrenheit of  $37.78\degree C?$  

•  $80\degree F$  

•  $90\degree F$  

•  $100\degree F$  

•  $110\degree F$  

Cath and Arvin are planning for their wedding. Cath suggested that she wants Casa de Aurora to cater their reception. The reception hall rental fee starts at a flat rate of Php3500 and an additional rental fee of Php60.00 per guest. If their budget is limited at Php20000.00, which of the following represents the total rental fee as a function of the number of guests?

• y = 3500 + 60x

• y = 3500 - 60x

• y = 60 + 3500x

• y = 60 - 3500x

Cath and Arvin are planning for their wedding. Cath suggested that she wants Casa de Aurora to cater their reception. The reception hall rental fee starts at a flat rate of Php3500 and an additional rental fee of Php60.00 per guest. If their budget is limited at Php20000.00, which of the following is the inverse function?

• $f^{-1}\left(x\right)=\frac{x-60}{2000}$

• $f^{-1}\left(x\right)=\frac{x+50}{3500}$
  

• $f^{-1}\left(x\right)=\frac{x+3500}{50}$
  

• $f^{-1}\left(x\right)=\frac{x-3500}{60}$

Cath and Arvin are planning for their wedding. Cath suggested that she wants Casa de Aurora to cater their reception. The reception hall rental fee starts at a flat rate of Php3500 and an additional rental fee of Php60.00 per guest. If their budget is limited at Php20000.00, What is its domain and range?

• D = {xϵN | 0≤x≤275}    and   R = {yϵR | 0≤y≤20000}

• D = {xϵN | 0≤x≤200}    and   R = {yϵR | 0≤y≤10000}
  

• D = {xϵN | 0≤x≤160}    and   R = {yϵR | 0≤y≤20000}
  

• D = {xϵN | 0≤x≤10000}    and   R = {yϵR | 0≤y≤20000}
  

Suppose I am travelling at 30 mi/hr, and i want to know how I have gone in x hours. Then, this could be represented by the function f(x) = 30x. Find the inverse of the function.

• $f^{-1}\left(x\right)=\frac{x}{10}$

• $f^{-1}\left(x\right)=\frac{x}{20}$

• $f^{-1}\left(x\right)=\frac{x}{30}$

• $f^{-1}\left(x\right)=\frac{x}{100}$

Marx is standing on the ground to take a series of photographs of a kite rising vertically. The distance between Luis at B and the launching point of the kite A is 800m. Luis must keep the kite on sight and therefore its angle of elevation must change with height x of the kite. Find the angle t as a function of the height x.

• $t=\tan^{-1}\left(\frac{x}{800}\right)$

• $t=\tan^{-1}\left(\frac{500x}{300}\right)$

• $t=\tan^{-1}\left(\frac{800x}{500}\right)$

• $t=\tan^{-1}\left(800\right)$

Marx is standing on the ground to take a series of photographs of a kite rising vertically. The distance between Luis at B and the launching point of the kite A is 800m. Luis must keep the kite on sight and therefore its angle of elevation must change with height x of the kite. Find the angle t in degrees when x is equal to 150 meters.

• 31.6

• 21.6

• 11.6

• 10.6