A function is defined by f(x)= e^(x^2+4), all real x. Find inverse of f(x) and its domain.

Let f(x)=y: y = e^(x²+4); To find the inverse of a function, you need to find x in terms of y. In this case, you need to bring the exponent to the base. So in order to bring x²+4 from the power, take natural log of both sides so: ln(y) = ln(e^(x²+4)); ln(e^(a)) = a, where a is some function. This means that: ln(y) = x²+4; Now that x is a base, the algebra becomes simple. Isolate x; x² = ln(y) - 4; Simplify; x = sqrt(ln(y) - 4); This is the inverse. However, to use the same terms as the original function let x = y and y = x, so; y = sqrt(ln(x)-4).