Let f be the function defined by f(x) = (1 + tanx)^(3/2) ...

[aleadley7]

Let f be the function defined by f(x) = (1 + tanx)^(3/2) for -(π/4) < x < (π/2).

a) Write an equation for the line tangent to the graph of f at the point where x = 0.

b) Using the equation found in part (a), approximate f(0.02).

c) Let f^(-1) denote the inverse function of f. Write an expression that gives f^(-1)(x) for all x in the domain of f^(-1).


I figured out the equation of the tangent line:
y - 1 = (3/2)x

but i'm not sure how to approximate values

and i also don't know how to take the inverse of f within the domain

 

[tkhunny]

Re: Let f be the function defined by f(x) = (1 + tanx)^(3/2)

b) Using the equation found in part (a), approximate f(0.02).

(3/2)*(0.02)+1

 

[tkhunny]

Re: Let f be the function defined by f(x) = (1 + tanx)^(3/2)

f(x) = (1 + tanx)^(3/2) for -(π/4) < x < (π/2).
I also don't know how to take the inverse of f within the domain

Find the inverse. Worry about the Domain later.

\(\displaystyle f^{-1}(x)\;=\;atan(x^{2/3}\;-1)\)