Advertisements
Advertisements
प्रश्न
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
Advertisements
उत्तर
We know that f(x) = `1/(x - 1)` is discontinuous at x = 1
Now, for x ≠ 1,
f(f(x)) = `"f"(1/(x - 1))`
= `1/(1/(x - 1) - 1)`
= `(x - 1)/(2 - x)`.
Which is discontinuous at x = 2.
Hence, the points of discontinuity are x = 1 and x = 2.
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
If y = log (cos ex) then find `"dy"/"dx".`
Find `dy/dx`, if `sqrt(x) + sqrt(y) = sqrt(a)`.
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
Find `"dy"/"dx"` if xey + yex = 1
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find `"dy"/"dx"` if, y = log(log x)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
The derivative of f(x) = ax, where a is constant is x.ax-1.
State whether the following is True or False:
The derivative of polynomial is polynomial.
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = x10, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"y)/("d"x)` = ex
Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`
If y = `2/(sqrt(a^2 - b^2))tan^-1[sqrt((a - b)/(a + b)) tan x/2], "then" (d^2y)/dx^2|_{x = pi/2}` = ______
If f(x) = `(x - 2)/(x + 2)`, then f(α x) = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
If f(x) = |cos x|, find f'`((3pi)/4)`
If y = log (cos ex), then `"dy"/"dx"` is:
If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
