Question

If `f( x ) = 2x + 3 and g ( x ) = 5- 2x`, what is `f(g(x))`?

Answer 1

`f(g(x)) = 13 - 4x`

Explanation:

To find `f(g(x))` we must substitute `color(red)(g(x))` for `color(red)(x) on the left side of the`f(x)`function and`color(red)(5 - 2x)`for each occurrence of`color(red)(x)`on the right side of the`f(x)# function.

`f(color(red)(x)) = 2color(red)(x) + 3` becomes:

`f(color(red)(color(red)(g(x)))) = 2(color(red)(5 - 2x)) + 3`

`f(color(red)(color(red)(g(x)))) = (2 xx 5) - (2 xx 2x) + 3`

`f(color(red)(color(red)(g(x)))) = 10 - 4x + 3`

`f(color(red)(color(red)(g(x)))) = 10 + 3 - 4x`

`f(color(red)(color(red)(g(x)))) = 13 - 4x`