1.Doesallfunctionshaveaninversefunction?No,onlyone-onefunctionhaveaninversefunction 2.Howtogettheinversefunctionofafunction?•Step1:Lety=thefunction•Step2:Rearrange(tofindx)•Step3:Swapxandy InverseFunct
A function that sends each input to a different output is called a one-to-one function. Definition We say a ff is a one-to-one function if f(x1)≠f(x2)f(x1)≠f(x2) when x1≠x2x1≠x2. One way to determine whether a function is one-to-one is by looking at its graph. ...
The graph of y = f –1(x) is the reflection in y = x of the graph of y = f (x).例题：To find the inverse of a function x → y (i) interchange x and y(ii) find y in terms of x.小试牛刀：
Now that we can find the inverse of a function, we will explore the graphs of functions and their inverses. Let us return to the quadratic function f(x)=x2f(x)=x2 restricted to the domain [0,∞)[0,∞), on which this function is one-to-one, and graph it as in Figu...
The function: f(x) = 2x+3 Put "y" for "f(x)": y = 2x+3 Subtract 3 from both sides: y-3 = 2x Divide both sides by 2: (y-3)/2 = x Swap sides: x = (y-3)/2 Solution (put "f-1(y)" for "x") : f-1(y) = (y-3)/2...
The graph of y=sin(x): The horizontal test fails. We need to restrict the domain to get the inverse function. (How about other parts?) Then it satisfies the horizontal line test, so it has an inverse f−1—sin−1(x) or arcsin(x). (Beware: the first of these notations is a...
The inverse f−1(x) is a reflection of the function f(x). Let us assume a point (a, b) on the graph of f, then the point (b, a) is on the graph of the inverse function f−1(x). We can identify the domain and range of a function f(x) from its graph. Example 4 G...
INVERSEFUNCTION–reversingafunction,“undoing”. f-1notatesaninversefunction.(not1/f) WHAT?? Findtheinverseoff(x)=4x-2 x *4 4x-2 -2 (x+2)/4 x /4 +2 So f-1(x)=(x+2)/4 Thingstonote.. Thedomainoff-1istherangeoff. Thegraphofaninversefunctioncanbefoundbyreflectingafunctionintheli...
➢f-1notatesaninversefunction.(not1/f)WHAT??Findtheinverseoff(x)=4x-2 x *4 -2 4x-2 (x+2)/4 /4 +2 x So f-1(x)=(x+2)/4 Thingstonote..➢Thedomainoff-1istherangeoff.➢Thegraphofaninversefunctioncanbe foundbyreflectingafunctionintheliney=x y=ex,y=xandy=lnx 5 4 y=ex...
designed, is simple in structure and low in cost, can vividly demonstrate the inverse function graph of the function, and can make students understand the graph position relation and the geometric significance of the function and the inverse function thereof in the same plane rectangular coordinate ...