W/c one of the ff functions is one to one correspondence?
A, f(x)=x+2 B, g(x)=x^2 C,h(x)=2x^2+4 D, none
B, g(x)=x^2, is not a one to one correspondence function.
To determine which of the given functions is a one-to-one correspondence, we need to check if each function satisfies the definition of a one-to-one correspondence.
A function is considered a one-to-one correspondence if each value of the domain maps to a unique value in the range, and no two different values in the domain map to the same value in the range.
Let's check the given functions one by one:
A) f(x) = x + 2:
To check if f(x) is a one-to-one correspondence, we can use the horizontal line test. If a horizontal line can intersect the graph of the function at more than one point, then the function is not one-to-one correspondence.
For f(x) = x + 2, the graph is a straight line, and any horizontal line intersects the graph at only one point. Therefore, function f(x) = x + 2 is a one-to-one correspondence.
B) g(x) = x^2:
The function g(x) = x^2 is not a one-to-one correspondence because multiple values in the domain can map to the same value in the range. For example, g(2) = 4 and g(-2) = 4, indicating that two different values in the domain (2 and -2) map to the same value in the range (4).
C) h(x) = 2x^2 + 4:
Similar to the function g(x) = x^2, the function h(x) = 2x^2 + 4 is also not a one-to-one correspondence. Again, multiple values in the domain can map to the same value in the range, making it violate the one-to-one correspondence definition.
D) None:
Based on our analysis, neither options B, C, nor D satisfy the condition for one-to-one correspondence. Only option A, f(x) = x + 2, is a one-to-one correspondence.
Therefore, the correct answer is A) f(x) = x + 2.