Determine order and degree(if defined) of differential y' + y =ex
y' + y =ex
y' + y - ex =0
The highest order derivative present in the differential equation is y'. Therefore, its order is one.
The given differential equation is a polynomial equation in y' and the highest power raised to y' is one. Hence, its degree is one.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Determine order and degree(if defined) of differential equation y' + 5y = 0
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
Let f: X → Y be an invertible function. Show that the inverse of f –1 is f, i.e., (f–1)–1 = f.
If f(x) = , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?