Answer:
Step-by-step explanation:
If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.
For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.
However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.
Answer:
See explanation below for further details.
Step-by-step explanation:
A rational consist of two real numbers such that:
If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.
If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example:
If and
, then:
If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example
If and
, then:
But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.
Example
If and
, then:
Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.
If and
, then:
Example
It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.
Example