Question

What is the funtion of fof; gog; given f(x)=3-5x and g(x)=1-3x?

Answer 1

Given functions are f (x ) = 3 - 5x and g (x ) = 1- 3x

1) ( f of  )(x ) = f (f (x ))

Substitute the expression for functioning f  (in this case 3 - 5x ) for f (x ) in the composition.

= f (3 - 5x )

Now substitute this expression (3 - 5x) in to function f  in place of the x  value.

= 3 - 5(3 - 5x )

= 3 - 15 + 25x

= 25x  - 12

2) ( g o g )(x ) = g (g (x ))

Substitute the expression for functioning g  (in this case 1 - 3x ) for g (x ) in the composition.

= g (1 - 3x )

Now substitute this expression (1 - 3x) in to function g  in place of the x  value.

= 1 - 3 (1 - 3x )

= 1 - 3 + 9x

= 9x - 2.

f of  = 25x  - 12 and g og = 9x - 2.