Question

Let g(x) be the inverse of f(x)=x^3+4^x+3. Calculate g(8) [without finding a formula for g(x)] and then calculate g′(8).

So this is what I got so far an stuck
8=y^1/3+y/4+1/3

23/4=y^1/3+y/4

Answer 1

Look....to find g(8)...just set x^3 + 4^x + 3 = 8
x^3 + 4^x = 5
x = 1 (just by inspection)
Now, calculate g'(8)

Answer 2

wait so you did not have to do the inverse unless doing derivative?

Answer 3

Exactly. Just a waste of time...besides in your problem it stated not to find a formula for g(x) which we didnt.

Answer 4

Oh ok, do I have to find the inverse when doing the derivative in this problem?

Answer 5

Let me be clear about what I am saying.........

If we have a function f, as given above, and we want the inverse function, g, at x = 8...we could have worked out algebraically and determine the inverse function, g, and then plug in 8.

I did NOT do that. I just said that take f itself and set it to 8 which is IDENTICAL to doing it the first way I just mentioned. Becuase the domain of a function equals the range of its inverse, and the domain of the inverse equals the range of the original function.

Answer 6

Oh ok gotcha I am going to try the derivative one now.