For the given functions f ,g and h, find f o g o h and state the exact domain of f o g o h. Please show all of your work.
F(x)=inx
g(x)=/x/-7
h(x)=5x+6
Is your question similar to Jo's ?
Did you mean F(x) = ln(x) ?
did you mean g(x) = |x| - 7 ?
http://www.jiskha.com/display.cgi?id=1326874213
follow Steve's method for your question.
1. no is said inx
2.yes
inx makes no sense
I bet it is ln x or ln(x) like in the other post
did you look at the link I gave you?
To find f o g o h (or the composition of functions), we'll start by substituting the function g into function f. Then, we'll substitute the result into function h.
Step 1:
Substituting g(x) into f(x) gives us:
f(g(x)) = f(|x| - 7)
Step 2:
Now, we substitute f(g(x)) into h(x):
h(f(g(x))) = h(f(|x| - 7))
Step 3:
To find the exact domain of f o g o h, we need to consider the restrictions imposed by each function.
The domain of f(x) is all real numbers, since the natural logarithm function is defined for all positive real numbers and zero.
The domain of g(x) is also all real numbers, as the absolute value function can take any real number as input.
The domain of h(x) is again all real numbers, as there are no restrictions on a linear function.
Step 4:
Now, we need to determine the domain of f(g(x)) and then the domain of h(f(g(x)).
To find the domain of f(g(x)), we look for values of x that make |x| - 7 non-negative. Since the absolute value function returns the non-negative value of its input, we have:
|x| - 7 ≥ 0
Adding 7 to both sides, we get:
|x| ≥ 7
This means that x can be any real number greater than or equal to 7 or any real number less than or equal to -7.
The domain of f(g(x)) is therefore (-∞, -7] ∪ [7, ∞).
Finally, since the domain of h(f(g(x))) is the same as the domain of f(g(x)), the exact domain of f o g o h is (-∞, -7] ∪ [7, ∞).