Use symmetry to graph the inverse of the function

Your answer would be positive 

The correct option is d.

Step-by-step explanation:

Let a function is f(x) and its inverse is f⁻¹(x). If both functions drawn on a coordinate plate than the graph of f(x) and f⁻¹(x) are mirror image of each other across the line y=x.

In other word the line y=x is the axis of symmetry of the graph of function and its inverse.

We need to find the correct graph that represent the function and its inverse.

Draw a line y=x in each graph as shown below.

From the below graph it is clear that only graph d represent the function and its inverse because both the functions are mirror image of each other across the line y=x.

Therefore the correct option is d.

a. is the correct option

The graph of a function [tex]f[/tex] and its inverse function [tex]f^{-1}[/tex] are related to each other. The relationship between these two graphs can be explained by taking a point [tex](a,b)[/tex] that is on the graph of [tex]f[/tex], then point [tex](b,a)[/tex] must lie on the graph [tex]f^{-1}[/tex] and vice versa meaning that the graph of [tex]f^{-1}[/tex] is a reflection of [tex]f[/tex] in the line [tex]y=x[/tex]. The only graph that meet this requirement is the option a. For instance, the point [tex](0,5)[/tex] is on the graph of [tex]f[/tex] while the point [tex](5,0)[/tex] is on the graph of [tex]f^{-1}[/tex] as indicated below.

Step-by-step explanation:

So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.

The correct option is a.

Step-by-step explanation:

If a function is defined as

[tex]f(x)=\{(x,y):x\in R,y\in R\}[/tex]

then the inverse of the function is

[tex]f^{-1}(x)=\{(y,x):x\in R,y\in R\}[/tex]

We know that the graph of a function and its inverse function symmetrical about the line y=x.

Draw the line of symmetry x=y in each of the given graph.

From the below figure it is clear that only graph 1 is symmetrical about the line y=x.

Therefore the correct option is a.