Question

If `f(x)=3x` and `g(x)=4x-3`, how do you find f[g(5)] and g[f(5)]?

Answer 1

Evaluate `a = g(5)` then substitute the value of `a` for the argument `g(5)` in `f(g(5))` and evaluate `f(a)` for this argument.
(Similarly for `g(f(5))`)

Explanation:

`f(x)=3x` `color(white)("XXXXXX")` `rarr` `color(white)("XXXX")` `f(5) = 15`

`g(x) = 4x-3` `color(white)("XXXX")` `rarr` `color(white)("XXXX")` `g(5) = 17`

`f(g(5)) = f(17)`
`color(white)("XXXX")` `= 3(17) = 51`

`g(f(5) = g(15)`
`color(white)("XXXX")` `= 4(15) -3 = 57`