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Monotonically Increasing Functions

Which of the ...

Question

Which of the following relations are functions
$f : {(2, 1), (3, 1), (4, 1)}$
$g : {(2, 2), (2, 4), (3, 3), (4, 4)}$
$h = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}$

A

f,g

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B

g,h

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C

h,f

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D

f,g,h

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Solution

The correct option is B h,f
f is a function, as all of the domain of f is associated with a unique element of codomain set.
g is not a function as $2$ is associated with the two distinct elements $2, 4$ .
h is a function, as reason is f.

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Similar questions

f, g

h

are differentiable functions. If

f (0) = 1; g (0) = 2; h (0) = 3

and the derivative of their pair wise products at

x = 0

(f g)^{'} (0) = 6; (g h)^{'} (0) = 4

(h f)^{'} (0) = 5

then compute the value of

(f g h)^{'} (0) .

(f^{2} - b c) x + (c h - f g) y + (b g + h f) z = 0

,

(c h - f g) x + (g^{2} - c a) y + (a f - g h) z = 0

,

(b g - h f) x + (a f - g h) y + (h^{2} - a b) z = 0

a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0

f, g

h

be differentiable functions. If

f (0) = 1,

g (0) = 2,

h (0) = 3

and the derivatives of their pairwise products at

x = 0

(f g)^{'} (0) = 6,

(g h)^{'} (0) = 4

(h f)^{'} (0) = 5,

then the value of

(f g h)^{'} (0)

Q. Which congruence criterion is used in the following?
Given:

∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G

Δ L M N ≅ Δ G F H

Q. If ax + hy + gz = 0, hx + by + fz = 0, prove that

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