Determining the values to make a function undefined.

For what values or range of values are the following functions undefined a) f(x) = 1/x b) g(x) = Square root of (x+2)(x-3)
c) h(x) = 5 / x^2-4x-45

Find the domain and range of the functions

State the domain and range for each of the following functions (a) f(x) = ln(1 + x squared) (b) f(x) = 1 / (over) x-1 + 1 / (over) x-2

A proof that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H, where (f,f) denotes the inner product on H.

Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that (Tf,f) is real-valued for all f in H.

Functions

There are two functions: f(x)=(x^2+x-12)/(x^2+6x+18) and g(x)=(x-3)/(x+2) If you take the first derivation of both functions, they should be equal. Please explain why.

Integrals: Cost function and Marginal Cost

Given ist the following cost function: k(x)=x^3-9x^2+29x+35 x= quantity k= cost question 1: At what quantity is the minimum of the marginal cost? question 2: What is the increase of cost if the production is increased from 3 to 4 (integral)?