Question

For all values of x.
f(x) = x - 1
and
g(x) = 2x*squared* + 3
Solve fg(x) = gf(x)​

Answer 1

Hey There

Here's The Answer

________________________

• Given :

• f(x) = x - 1
• g(x) = 2x² + 3

• To Show : f( g(x) ) = g( f(x) )

• L.H.S.

=> f( g(x) ) = f ( 2x² + 3 )

=> f ( 2x² + 3 ) = 2x² + 3 - 1

=> f ( 2x² + 3 ) = 2x² + 2

• R.H.S.

=> g( f(x) ) = g ( x - 1 )

=> g ( x - 1 ) = 2 ( x - 1 )² + 3

=> g ( x - 1 ) = 2 ( x² + 1² - 2x ) + 3

=> g ( x - 1 ) = 2x² + 2 - 4x + 3

=> g ( x - 1 ) = 2x² + 2 - 4x + 3

=> g ( x - 1 ) = 2x² - 4x + 5

• Hence, L.H.S. ≠ R.H.S.

Hope It Helps.