Question

Let A = `{3/5}` and B = `{7/5}` Let f: A → B: f(x) = `(7x + 4)/(5x - 3)` and g:B → A: g(y) = `(3y + 4)/(5y - 7)` then (gof) is equal to

Options

• I_B

• I_A

• I_B and I_A

• Neither I_A nor I_B

Answer 1

I_A 

Explanation:

Let x ∈ A, Then,

(of) (x) = g[f(x)] = `g((7x + 4)/(5x - 3))`

= g(y), Where y = `(7x + 4)/(5x - 3)` ......(i)

= `(3y + 4)/(5y - 4) = (3((7x + 4)/(5x - 3)) + 4)/(5((7x + 4)/(5x - 3)) - 7)`

= `((21x + 12 + 20x - 12))/((5x - 3)) xx ((5x - 3))/((35x + 20 - 35x + 21))`

`(41x)/41 = x = I_A(x)`.