Question

Use abs(x) for x\.

Given that f(x) = |x| and g(x) = 9x + 2, calculate
(a) fog(x)=
(b) go f(x)=
(c) fo f(x)=
(d) go g(x)=

Answer 1

The results are f(g(x)) = |9x + 2|, g(f(x)) = 9|x| + 2, f(f(x)) = |x|, and g(g(x)) = 81x + 20.

Step-by-step explanation:

The task is to find the composite functions of given functions f(x) = |x| and g(x) = 9x + 2. Let's calculate each of the composite functions step by step.

(a) f of g(x) = f(g(x))

First, plug g(x) into f(x):

f(g(x)) = f(9x + 2) = |9x + 2|.

(b) g of f(x) = g(f(x))

Now, plug f(x) into g(x):

g(f(x)) = g(|x|) = 9|x| + 2.

(c) f of f(x) = f(f(x))

Plug f(x) back into itself:

f(f(x)) = f(|x|) = ||x|| = |x|, in which the double absolute value does not change the result because absolute values are always non-negative.

(d) g of g(x) = g(g(x))

Finally, plug g(x) into g(x):

g(g(x)) = g(9x + 2) = 9(9x + 2) + 2 = 81x + 20.