Hi there, I need help with composition of functions.
I need to find fog, gof, gog, and fof and their domains for the following:
f(x) = square root of 2x +3
g(x) = x^2 + 1
if someone can help me asap that would be so great!
For g of f, substitute sqrt(2x +3) for x in g(x)
You get (2x + 3) + 1 = 2x + 4
The domain is all numbers in thnis case.
Do the others the same way. We will gladly critique your work.
okay, so i tried out subtsting x into f (x) and i got sqrt (2x^2 +5)..is that right?
and what do u mean domain is all in numbers?
can u help me with the f o f and g og?
and a side question, we got a table of values that was something like
x 1 2 3 4 5 6
f(x) 3 1 .....
g(x) 6
so the first question is like evaulaute:
f(g(1))
would that be
3(6)?
Are you trying to calculate f of g(x)?
Assuming f(x) = sqrt(2x+3) and not sqrt (2x) + 3, f of g(x) would be
sqrt [2(x^2 +1) + 3]= sqrt (2x^2 + 5)
So you would be correct.
g of g(x) = (x^2+1)^2 +1 = x^2 + 2x + 2
To your side question: yes, the first answer is 18.
Of course! I'd be happy to help you with composition of functions. Let's start by defining the given functions:
f(x) = √(2x + 3)
g(x) = x^2 + 1
To find the composition of functions f o g, g o f, g o g, and f o f, we need to substitute the functions into each other.
1. f o g:
To find f o g, we substitute g(x) into f(x):
f o g(x) = f(g(x))
= f(x^2 + 1)
= √(2(x^2 + 1) + 3)
= √(2x^2 + 2 + 3)
= √(2x^2 + 5)
The domain of f o g depends on the domain of g(x) since we substituted g(x) into f(x). Since the domain of g(x) is all real numbers, the domain of f o g is also all real numbers.
2. g o f:
To find g o f, we substitute f(x) into g(x):
g o f(x) = g(f(x))
= g(√(2x + 3))
= (√(2x + 3))^2 + 1
= (2x + 3) + 1
= 2x + 4
The domain of g o f depends on the domain of f(x) since we substituted f(x) into g(x). The given function f(x) is the square root of (2x + 3), and the radicand (2x + 3) must be non-negative for the square root to be defined. So, the domain of g o f is all real numbers greater than or equal to -3/2 (to make 2x + 3 non-negative).
3. g o g:
To find g o g, we substitute g(x) into itself:
g o g(x) = g(g(x))
= g(x^2 + 1)
= (x^2 + 1)^2 + 1
= x^4 + 2x^2 + 2
The domain of g o g is the same as the domain of g(x), which is all real numbers.
4. f o f:
To find f o f, we substitute f(x) into itself:
f o f(x) = f(f(x))
= f(√(2x + 3))
= √(2(√(2x + 3)) + 3)
= √(4x + 6 + 3)
= √(4x + 9)
The domain of f o f is the same as the domain of f(x), which is all real numbers greater than or equal to -3/2 (to make 2x + 3 non-negative).