Identifying inverse functions and finding inverses
State if the given functions are inverses:
g(x) = 4 - (3/2)x
f(x) = (1/2)x + (3/2)
No.
What is a one-to-one function?
A function is one-to-one if each element in the range corresponds to exactly one element in the domain.
What is the horizontal line test?
A technique used to test if a function is one-to-one where if any horizontal line drawn on a graph intersects the graph of the function more than once that function is not one-to-one.
Find the inverse function of f(x) = x5 + 6.
f^-1(x) = 5√x - 6
State if the given functions are inverses:
f(n) = (-16 + n)/4
g(n) = 4n + 16
Yes.
Is function f defined by f = {(1 , 2),(3 , 4),
(5 , 6),(8 , 6),(10 , -1)},
a one to one function?
Two different values in the domain, namely 5 and 6, have the same output; hence function f is not a one to one function.
Determine whether this function passes the horizontal line test and explain why.
f(x) = 1 / (x - 2)2
No. Because the graph is being cut at more than one point.
Find the inverse function of f(x) = x3 - 18.
f-1(x) = 3√x+ 18
Find the inverse of the function:
g(x) = (7x + 18)/2
g^-1(x) = (2x - 18)/7
Is function f given by f(x) = -x3 + 3 x2 - 2,
a one to one function?
Since a horizontal line cuts the graph of f at 3 different points, that means that they are at least 3 different inputs with the same output Y and therefore f is not a one to one function.
Define an inverse function.
A function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x. In math, if ƒ is a function from a set A to a set B, then an inverse function for ƒ is a function from B to A.