Question

Let f(x)=8x-1, and g(x)=x/2 how do you find (fg(x))?

Answer 1

Write `f(u) = 8u-1`, then substitute `u = g(x)` to get:

`f(g(x)) = f(u) = 8u - 1 = 8g(x) - 1 = 8(x/2)-1`

`= 4x-1`

Explanation:

It's slightly easier to see if you use a different variable name for the definition of `f`, for example `f(u) = 8u-1`. Note that the variable name does not really matter - it is just a place-holder for a value.

Then substitute `u = g(x)` to get:

`f(g(x)) = f(u) = 8u - 1 = 8g(x) - 1 = 8(x/2)-1`

`= 4x-1`

Alternatively, describe `f(g(x))` as a sequence of steps, then construct a formula from those steps to simplify:

(1) Divide by `2`
(2) Multiply by `8`
(3) Subtract `1`

So `f(g(x)) = (x/2)*8 - 1 = 4x-1`