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The function f(x) = 2x is
- a)one-one mapping
- b)one-many
- c)many-one
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The function f(x) = 2x isa)one-one mappingb)one-manyc)many-oned)none o...
One-One Mapping
A function is said to be one-one or injective if each element of the domain is mapped to a unique element in the range. In other words, no two elements in the domain are mapped to the same element in the range.
Explanation
The function f(x) = 2x is a linear function, which means it has a constant rate of change. This function maps each element in the domain to a unique element in the range, as shown below:
Domain: {-3, -2, -1, 0, 1, 2, 3}
Range: {-6, -4, -2, 0, 2, 4, 6}
As we can see, each element in the domain is mapped to a unique element in the range. For example, f(-3) = -6, f(-2) = -4, f(-1) = -2, f(0) = 0, f(1) = 2, f(2) = 4, and f(3) = 6.
Therefore, the function f(x) = 2x is a one-one mapping.
A function is said to be one-one or injective if each element of the domain is mapped to a unique element in the range. In other words, no two elements in the domain are mapped to the same element in the range.
Explanation
The function f(x) = 2x is a linear function, which means it has a constant rate of change. This function maps each element in the domain to a unique element in the range, as shown below:
Domain: {-3, -2, -1, 0, 1, 2, 3}
Range: {-6, -4, -2, 0, 2, 4, 6}
As we can see, each element in the domain is mapped to a unique element in the range. For example, f(-3) = -6, f(-2) = -4, f(-1) = -2, f(0) = 0, f(1) = 2, f(2) = 4, and f(3) = 6.
Therefore, the function f(x) = 2x is a one-one mapping.
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Community Answer
The function f(x) = 2x isa)one-one mappingb)one-manyc)many-oned)none o...
F(x)=2x is a function
if we take x={1,2,3,4...}(A)
we get {2,4,6,8...}(B)
so every image in(A)has a unique range in(B)
so this is the one-one mapping
if we take x={1,2,3,4...}(A)
we get {2,4,6,8...}(B)
so every image in(A)has a unique range in(B)
so this is the one-one mapping
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