Perform the following operation on the listed problem (a) fog (x) & (b) gof (x);

Question

f(x) = 2x + 1 g(x) = 3x - 2
Thank you so much!

Answer 1

Given functions are f (x ) =  2x + 1 and g (x ) = 3x - 2

a ) ( f og )(x ) = f  (g (x ))

Substitute the expression for functioning g (in this case 3x - 2 ) for g (x ) in the composition.

= f (3x - 2)

Now substitute this expression (3x - 2) in to function f  in place of the x  value.

= 2(3x - 2) + 1

=  6x - 4 + 1

= 6x - 3

b) (g of  )(x ) = g (f (x ))

Substitute the expression for functioning f  (in this case 2x + 1 ) for f  (x ) in the composition.

= g (2x  + 1 )

Now substitute this expression (2x + 1) in to function g in place of the x  value.

= 3(2x + 1 ) - 2

= 6x + 3 - 2

= 6x + 1

(f og )(x ) = 6x - 3 and (g of  )(x )  = 6x + 1.