(a) `f(x)=2x + 5`

`y = 2x + 5`

To determine the inverse function, interchange x and y.

`x=2y+5`

Then, isolate y.

`2y=x-5`

`y=(x-5)/2`

Replace y with `f^(-1)(x)` , to indicate that it is the inverse of the given function.

`f^(-1)x = (x-5)/2`

(b) To check that `f^(-1)x = (x-5) / 2` is the inverse of `f(x)= 2x+5` , let

the inverse function be `g(x) = (x-5)/2` .

Note that if `(f o g (x) )= (g o f)(x)` , then f(x) and g(x) are inverses of each other.

So,

` (f o g (x) ) = (g o f)(x)`

`f ( g(x) ) = g(f(x))`

At the left side, replace the x in f(x) with (x-5)/2. And at the right side, replace the x in g(x) with 2x+5.

`2((x-5)/2) +5 = (2x+5-5)/2`

`x-5 + 5 = 2x/2`

`x = x`

**Hence, `g(x) = (x-5)/2` is the inverse function of `f(x) = 2x +5` .**

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