I think you're misinterpreting the question, and trying to do more than they want. Did you notice that they don't even tell you that the balloon is spherical? As I read it, they want you to take nothing as given except the (unspecified) functions f and g.Hi! I'm a bit confused about question 69.
I know that in question 67, the answer is v = 4/3 * pi * f(t)^3
and that 68 is 8v given that the radius is increased x2
However, in question 69 they never gave the function of f(t) so I'm confused about how I should go about it
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Yes, #67 is just the composite function g(f(t)); and #68 might be intended to be either your g(2f(t)), or just g(2r). I'm not sure.If I don't know the functions f and g, how will I be able to solve question 69?
The only information I can use in that case is f(t) = 30
Also then I'm guessing the answer for question 68 is simply V = g(2(f(t))
and for 67 it's V = g(f(t))
Yes, we've done inverse functions.Yes, #67 is just the composite function g(f(t)); and #68 might be intended to be either your g(2f(t)), or just g(2r). I'm not sure.
For #69, you want the value of t for which f(t) = 30. Have you learned about inverse functions yet?
Then #70 will be similar.
As you've guessed, my impression is that this exercise is all about using function notation. I'd be a little more sure if I were tutoring you side by side, and could look at your textbook or notes to see what has been taught most recently, what examples were given, and what other exercises precede and follow this, all of which would provide further context.
What do the asterisks represent? I suppose you probably mean that that value of r is what you want to use in the next line.Yes, we've done inverse functions.
So f^-1(30) = t, for 69?
Oooohhh and so
g(f(t)) = 100,000
g^-1(100,000) = f(t)*
f^-1(r)* = t
Is that it? The notation's a bit messy so could you recommend a better way of writing it?