Question

If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is ____________.

Options

• a constant function

• an exponential function

• an even function

• an identity function

Answer 1

If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is an identity function.

Explanation:

We have, f(x) = `(2"x" + 3)/(3"x" - 2)`

fof = f(f(x)) = `(2"f"("x") + 3)/(3"f"("x") - 2)`

fof = `(2((2"x" + 3)/(3"x" - 2)) + 3)/(3((2"x" + 3)/(3"x" - 2)) - 2)`

fof = `(4"x" + 6 + 9"x" - 6)/(6"x" + 9 - 6"x" + 4)`

fof = `(13"x")/13` = x = an identity function