how to varify algebraically if a function is inverse?

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Oct 3rd, 2015

I'm here to help. Ask as many questions as you like. I'm not afraid of questions.

Basically a function is inverse of the other, if that function can be substituted into the other, and the result be simply x. 

For example, say the function is f(x)=2x. and the other function is g(x)=3x-8. When you plug in either equation in place of x, if you simplify it should only be x left. 

So f(g(x))=2(3x-8)


6x-16 isn't x.

These functions are not inverses of eachother. 

But to the one you asked about:

f(x)=1/7x + 2/7

g(x)=7x - 2.

f(g(x))=1/7 (7x - 2) + 2/7

f(g(x))=7/7x - 2/7 + 2/7



So when function g(x) is substituted into f(x), the remaining value is simply x. 
No we have to plug f(x) into g(x) to see if we just get x.

g(f(x))=7(1/7x + 2/7) -2

7/7x + 14/7 - 2

7/7= 1



Which means g(f(x))=x.

These two functions are inverses of eachother. 

I know math can be difficult. I have different ways of thinking, so I had a hard time in all my math classes. 
Math can be difficult, but if you need help in the future, let me know. Email me:

Take care partner.

-Doctor Turner

Glad to help. If you need further clarification, let me know. -Doctor Turner
Sep 20th, 2015

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