How do you do these questions?

Step-by-step explanation:

(a)

g(x) = d/dx [2/√π ∫₀ˣ e^(-t²) dt]

g(x) = 2/√π e^(-x²)

g(-x) = 2/√π e^(-(-x)²) = 2/√π e^(-x²)

g(-x) = g(x)

Therefore, g(x) is even.

(b)

erf(x) = 2/√π ∫₀ˣ e^(-t²) dt

erf(x) = ∫₀ˣ g(t) dt

erf(-x) = ∫₀⁻ˣ g(t) dt

erf(-x) = -∫₋ₓ⁰ g(t) dt

Since g(t) is even, it is symmetrical about x=0.

erf(-x) = -∫₀ˣ g(t) dt

erf(-x) = -erf(x)

2t+4

step-by-step explanation:

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.