Final Exam Study Guide: (fog)(-9), inverse fcn, variation

[Tyler Durdan]

I am working on my final exam study guide for college algebra and have a few I need help with.

1) "Fill in the blank. Given that f(x) = -4x-2 and g(x)=x^2=9. (fog)(-9)= ?

2) "Find the inverse of the funtion f(x)= 3x-5/6. Then Fill in the blank below. F^-1(x)= ?

3) The intensity of illumination from a light source varies inversley with square of the distance from the source. Suppose that a reading lamp has an intensity of 5000 lumens at a distance of 4 feet.

a) The intesnity of the lamp is how many lumens at a distance of 2 feet?

b) The intensity of the lame is 300 lumens at a distnace of how many feet?

 

[jonboy]

Hi Tyler. I'll give you a few hints.

"Fill in the blank. Given that f(x) = -4x-2 and g(x)=x^2=9. (fog)(-9)= ?

Do you know what (f o g) means?

It means insert g(x) for x in f(x)

Then once you find (f o g) insert a 9 for x and solve.

BTW I think you have one extra = in your function for g (x).

"Find the inverse of the funtion f(x)= 3x-5/6. Then Fill in the blank below. F^-1(x)= ?

First rename f (x) as y in: f(x) = 3x - 5/6

Then switch x and y: y = 3x - 5/6 => x = 3y - 5/6

Solve for the new y, which will be f^-1(x).