0
Still curious? Ask our experts.
Chat with our AI personalities
Devin
Coach
ReneAdd your answer:
Earn +20 pts
Does every function have an inverse that is a function?
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.
What is the inverse of y x2?
Y = X2 Inverse. Y = 1/X2 ======
Is the inverse of the function y equals x2 still a function?
No. If you invert that function, it will produce an equation that gives you two return values for one input value. This does not meet the definition of a function.
What is inverse of a function?
Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2
What kind of symmetry indicates that a function will not have an inverse?
If a function is even ie if f(-x) = f(x). Such a function would be symmetric about the y-axis. So f(x) is a many-to-one function. The inverse mapping then is one-to-many which is not a function. In fact, the function need not be symmetric about the y-axis. Symmetry about x=k (for any constant k) would also do. Also, leaving aside the question of symmetry, the existence of an inverse depends on the domain over which the original function is defined. Thus, y = f(x) = x2 does not have an inverse if f is defined from the real numbers (R) to R. But if it is defined from (and to) the non-negative Reals there is an inverse - the square-root function.
