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：
1.Doesallfunctionshaveaninversefunction?No,onlyone-onefunctionhaveaninversefunction 2.Howtogettheinversefunctionofafunction?•Step1:Lety=thefunction•Step2:Rearrange(tofindx)•Step3:Swapxandy InverseFunctions Graphinginversefunctions InverseFunctionsConsiderthegraphofthefunction f(x)2x4 y2x...
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...
Addition inside Function: horizontal shifts, h This shifts the original function y=f(x)y=f(x) to y=a⋅f(bx−h)+ky=a⋅f(bx−h)+k Combining Transformations based on the Order of TransformationsFor example, the graph of a function could be stretched by a factor of 2, moved h...
When working with theinverse of a function, we learned that the inverse of a function can be formed by reflecting the graph over the identity liney = x. We also learned that the inverse of a function may not necessarily be another function. ...
【题目】T he graph of a function and its inverseFor each of the following functions, work outthe inverse function, and draw the graphs ofboth the original and the inverse on the sameaxes, using the same scale on both axes.(i) f(x)=x^2 , x∈R^+(i) f(x)=2x, x∈R(i)f(x)...
Is the inverse of a function always a function? To answer that question let's look at the function in Diagram 1. In that graph, you can see the original function and its inverse . Is the inverse of that function , also a function? Show Answer No As you can see, the inverse...
A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called the rainbow connection number ...
· ... However, you may not be able 10 obtain the complete graph of -" = x2l3 by entering )') = x f\ (2/3). If nOI. you should use YI = (x /\ (1/3»- or YJ=~' EXAMPLE 4 Verifying Inverse Functions Algebraically 5 Which of Ihe functions is the inverse of I(x) :...
So the inverse of: 2x+3 is: (y−3)/2The inverse is usually shown by putting a little "-1" after the function name, like this:f-1(y)We say "f inverse of y"So, the inverse of f(x) = 2x+3 is written:f-1(y) = (y-3)/2...