Question

Let f: R- R be defined by f(x) = 10x + 7. Find a function g: R- R such that
gof= fog = Ir

Answer 1

Function, f(x) = 10x +7
To get the inverse of function, f(x). we have to check weather it is one-one function and onto function or not.

(1) one-one function
Let x1 and x2 ∈ R
then f(x1) = f(x2)
⇒10(x1)+7 = 10(x2) +7
⇒x1 = x2
Hence f(x) is one-one function.

(2) Onto function
f(x) = 10x +7
⇒y = 10x+7
⇒10x =y -7
⇒x= (y-7)/10
it shows that for every value of y ∈ R, we will find an x ∈ R
such that,
f(x) = f[(y-7)/10]
      = 10(y-7)/10 + 7 = y
Hence f(x) is onto function.

so, f inverse(y) = (y-7)/10
this is our required function, 
So required function, g(x) =(x-7)/10

Answer 2

Answer: hope it helps

Step-by-step explanation:Function, f(x) = 10x +7

To get the inverse of function, f(x). we have to check weather it is one-one function and onto function or not.

(1) one-one function

Let x1 and x2 ∈ R

then f(x1) = f(x2)

⇒10(x1)+7 = 10(x2) +7

⇒x1 = x2

Hence f(x) is one-one function.

(2) Onto function

f(x) = 10x +7

⇒y = 10x+7

⇒10x =y -7

⇒x= (y-7)/10

it shows that for every value of y ∈ R, we will find an x ∈ R

such that,

f(x) = f[(y-7)/10]

      = 10(y-7)/10 + 7 = y

Hence f(x) is onto function.

so, f inverse(y) = (y-7)/10

this is our required function, 

So required function, g(x) =(x-7)/10