Graph each function f(x) and its inverse g(x). Then graph (f•g)(x)

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#1

Graph each function f(x) and its inverse g(x). Then graph (f•g)(x)

Answer:

since no function is defined i’m going to make up one and call it f(x) and then find its inverse and label it g(x). The composition of a function and its inverse should always be the equation of the line y=x .

so… suppose we

let f(x)=2x-1

to find its inverse

replace f(x) with variable y.
y=2x-1

then sway the x and y and the solve the equation back to the variable y

x=2y-1

y=(x+1)/2

now lets call this new y our g(x)

the composition of the functions (f*g)(x) can also be understood better as f(g(x))

where we essentially put the the function g(x) inside of f(x) and after doing some simplifying we will get f(x)=x , or also known as y=x. which happens to be the axis of symmetry that f(x) will reflect across when becoming g(x).