find functions f anf g so that fog equals H
H(x)=�ãx^2+17
please show work
if h(x) = √(x^2+17)
f(x) = √x
g(x) = x^2+17
f◦g = f(g(x)) = √g(x) = √(x^2+17) = h(x)
To find functions f and g such that fog(x) equals H(x) = x^2 + 17, we need to understand the concept of composition of functions.
The composition of two functions, f and g, denoted as fog(x), is formed by plugging the output of g into f. Mathematically, fog(x) = f(g(x)).
Let's proceed step by step to determine the functions f and g.
Step 1: Identify the inner function, g(x).
We can see that the term "x^2" appears in H(x), so let's let g(x) = x^2.
Step 2: Determine the outer function, f(x).
To find the function f(x), we need to consider the remaining part of H(x), which is "+ 17". This tells us that f(x) should add 17 to its input.
Step 3: Form the composition function, fog(x).
Now we can substitute g(x) and f(x) into the composition formula fog(x) = f(g(x)).
fog(x) = f(g(x))
= f(x^2)
= (x^2) + 17
So, the functions f and g such that fog(x) equals H(x) = x^2 + 17 are:
g(x) = x^2
f(x) = x + 17
I hope this explanation helps you understand how to determine the functions f and g in a composition of functions problem!