# f(x)=10x-10 find the value of (f^-1*f)(10)

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### 1 Answer

The composition of an inverse and its function is just x. That is `f^{-1} circ f(x)=x` . In this case, this means that for `f(x)=10x-10` then `f^{-1} circ f(10)=10` . We can verify this by calculating the inverse through interchanging x and y then solving for y:

`y=10x-10` interchange x and y

`x=10y-10` isolate y

`x+10=10y` divide by 10

`{x+10}/10=y`

This means that the inverse function is `f^{-1}(x)={x+10}/10` .

Now calculate explicitly the composition:

`f^{-1} circ f(10)`

`=f^{-1}(f(10))`

`=f^{-1}(10(10)-10)` simplify the argument

`=f^{-1}(100-10)` further simplify

`=f^{-1}(90)` now sub into the inverse

`={90+10}/10` simplify

`=10`

**The composition of the function and its inverse is 10.**