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
Find `"dy"/"dx"` if ex+y = cos(x – y)
Find `"dy"/"dx"` if, y = `root(3)("a"^2 + "x"^2)`
Find `"dy"/"dx"` if, y = log(log x)
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
State whether the following is True or False:
The derivative of polynomial is polynomial.
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
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 = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
If f(x) = `(x - 2)/(x + 2)`, then f(α x) = ______
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
If `sqrt(1 - x^2) + sqrt(1 - y^2) = a(x - y)`, prove that `(dy)/(dx) = sqrt((1 - y^2)/(1 - x^2))`.
y = `cos sqrt(x)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+4)`
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
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 ,
`x= e^(3t) , y = e^(4t+5)`
lf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, such that the composite function y = f[g(x)] is a differentiable function of x, then prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
If y = `log((x + sqrt(x^2 + a^2))/(sqrt(x^2 + a^2) - x))`, find `dy/dx`.
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`
