Question

Help with the function question please?

Let `f(x) = 2x+7 and g(x) = 3x+c`. Find `c` if `f(g(x)) = g(f(x))` for all values of `x`.

Answer 1

`f(g(x))=g(f(x))` if `c=14`

Explanation:

As `f(x)=2x+7` and `g(x)=3x+c`

hence `f(g(x))=f(3x+c)=2(3x+c)+7=6x+2c+7`

and `g(f(x))=g(2x+7)=3(2x+7)+c=6x+21+c`

It is apparent that generally `f(g(x))!=g(f(x))`

However, in this case we are having another variable `c`

and as `6x+2c+7=6x+21+chArrc=14`

Hence in a particular case

when `c=14`, we may have `f(g(x))=g(f(x))`