Question

If f : R → R and g : R → R are defined by f(x) = 3 x - 1, g(x) = x² + 1 then findi. fof (x² + 1)ii. fog (2)iii. gof (2a - 3)

Answer 1

HELLO DEAR,



GIVEN:- If f : R → R and g : R → R are defined by f(x) = 3 x - 1, g(x) = x² + 1


( 1 ) (fof)(x² + 1)

=> f{f(x² + 1)}

=> f{3(x² + 1) - 1}

=> f(3x² + 2)

=> 3(3x² + 2) - 1

=> 9x² + 6 - 1

=> 9x² + 5


( 2 ) (fog)(2)

=> f{g(2)}

=> f(x² + 1)

=> 3(x² + 1) - 1

=> 3x² + 3 - 1

=> 3x² + 2


( 3 ) (gof)(2a - 3)

=> g{f(2a - 3)}

=> g{3(2a - 3) - 1

=> g(6a - 10)

=> (6a - 10)² + 1

=> 36a² + 100 + 120a + 1

=> 36a² + 120a + 101


I HOPE IT'S HELP YOU DEAR,
THANKS