verify that a pair of functions are inverses?

Question

Using WolframAlpha, verify that the pair of functions below are inverses of each other.

 

f(x)=4x+10

g(x)=1/4x −5/2

 

how do i do this?

Answer 1

Here is the inverse function test: Is f(g(x)) = x ? If it is, then they are functions.

 

So here are the steps using this test:

 

Given f(x)=4x+10 and g(x)=1⁄4x-5⁄2

 

Evaluate f(g(x))

 

f(1⁄4x-5⁄2)=4(1⁄4x-5⁄2)+10

               =4/4x-20/2+10

               =1x-10+10

               =x+0

               =x

Since f(g(x))=x, the functions are inverses.

Answer 2

1.first put f(x)=y i.e.   y= 4x+ 10

2.second find the value of x as a function of y. i.e.   y=4x+ 10

                                                                      y-10 =4x

                                                                      (y-10)4 = x

                                                                     or  x = (1/4)y -5/2

3.now we get a function of y let it be g :     g(y) = (1/4)y - 5/2

4.last step to replace all the y by variable x  : g(x) = (1/4)x-5/2

 

these all are the steps to find the inverse function. Therefore the obtained function g(x) is the inverse function of the function 

f(x)=4x+10

in similar way you can show that f(x) is inverse of g(x)