Inverse function SIMPLE problems...ten points for best answer?

Question

I just wanna make sure I'm right!

1. If T=f(H) is time in minutes to bake a ckae @ H degrees F, what is the meaning and units of the inverse function?

2. A population is given in the formula P=f(t)=20+0.4t where P is the # of people (thousands) and t is the number of years since 1970. Evaluate the following quantities!

a. Evaluate f(25) and explain in word what it tells u about the population.

b. Determine f^-1

c. Evaluate f^-1(25) and explain in word what it tells u about the population.

3. Determine the inverse of f(x)=3x+1/x-2


LASTLY...

Give a prectical interpretation of the function:
f(h(t)), where A=f(r) is the area of a circle of radius r and r=h(t) is the radius of the circle at time t.

Please answer as many as possible.

THANKS

Ha, I barely had enough room though to write anything else!:-)

I'm just always paranoid with all of my work!

Ha, I barely had enough room though to write anything else!:-)

I'm just always paranoid with all of my work!

Answer 1

If you want us to make sure you're right, shouldn't you also post YOUR answers?

Answer 2

a million. it isn't any longer one-to-one. via fact it somewhat is a parabola while graphed, each and each y-fee has 2 x-values. It fails the horizontal line attempt. 2. f(r) = 4?r^2 i'll replace f(r) to y and r to x, in simple terms which you may see what is going on.... y = 4?x^2 so which you will desire to discover the inverse we swap x and y and then remedy for y. x = 4?y^2 x over (4?) = y^2 Sqrt of [x over (4?)] = y f -a million(r) = Sqrt of [r over (4?)] it is the inverse function. the fee? once I graph a sq. root function, there are no values in the fourth quadrant. A function and its inverse could have turn-flopped x- and y-values (if a function has a value of three, 4 in it, then its inverse could have 4, 3) so it somewhat is not inevitably genuine for this reason. a real inverse may be a facet-techniques parabola, polishing off the sq. root function.

Answer 3

The inverse function is H=g(t), or if you want to bake a cake in t minutes, you bake it at H degrees.
(mathemeticians make lousy cooks for this reason).

The population question
f(25) is the population estimate in 1995. Subst. in t-40, population=30 (30,000). The inverse (given P, find t) would be (P-20)/0.4. f-1(25) would equal 12.5 years from the inverse relation above.