Step-by-step explanation:

Given that,

[tex]\sf \: f(x) = 2x + 5 \\ \\ [/tex]

and

[tex]\sf \: g(x) = \dfrac{x - 5}{2} \\ \\ [/tex]

Now, we have to prove that fog(x) is identity function.

That means, we have to prove that fog(x) = x.

So, Consider

[tex]\sf \: fog(x) \\ \\ [/tex]

[tex]\sf \: = \: f[ g(x)] \\ \\ [/tex]

[tex]\sf \: = \: f\bigg(\dfrac{x - 5}{2} \bigg) \\ \\ [/tex]

[tex]\sf \: = \: 2\bigg(\dfrac{x - 5}{2} \bigg) + 5 \\ \\ [/tex]

[tex]\sf \: = \: x - 5 + 5 \\ \\ [/tex]

[tex]\sf \: = \: x \\ \\ [/tex]

Hence,

[tex]\sf\implies \sf \: fog(x) = x \\ \\ [/tex]

[tex]\sf\implies \sf \: fog(x) \: is \:an \: identity \: function. \\ \\ [/tex]