F(x) and g(x) functions help please?

Question

I'm not sure how to do this because of the g(x). Normally it's not just one number. How would I plug anything into it when it's one number? Thank you!

 

f(x) = |x|, g(x) = −7


(b) Find (g of f)(x).


(c) Find f(g(−2)).


(d) Find g(f(3)).

 

 

Answer 1

Hi Sky,

This is the expression of a function in terms of another function. 

 

f(x) = |x|, g(x) = −7
Note here that, although not written explicitly, it is meant that g(x) = { -7, for all x; therefore g(-2) = -7
(a) Find (g of f)(x).
       (g of f)(x)= g(f(x))
                     = g(|x|)

                     = -7
(b) Find f(g(−2)).

f(g(-2)) = f(-7)

           =|-7|

           = 7

           
(c) Find g(f(3)).

  g(f(3)) = g(|3|)

            = -7