Question 1
A)
f(x)=2^x and g(x)=3−x
I got 3x^2+12 don't know if im right
B) i need help for this
f(x)=sinx and g(x)=x
You got 3x^2 + 12 , but what was the question ???
Are you supposed to find something like f(g(x)) ?
Are you solving ?
Finding the composite function
Still not totally clear what you mean, is it
f(g(x)) or g(f(x)) ------ not the same!
I will assume
f(g(x))
= f(3-x)
= 2^(3-x)
I have no idea how you got 3x^2 + 12
same with B
if f(x) = sinx and g(x) = x
then
f(g(x))
= f(x)
= sinx
For question 1A, you mentioned that you got the answer 3x^2+12. However, that does not match the given functions f(x)=2^x and g(x)=3−x. To find the result of combining the functions, you should follow these steps:
1. Start by writing the composition of the two functions:
(f ∘ g)(x) = f(g(x))
2. Substitute g(x) into f(x):
f(g(x)) = 2^(g(x))
3. Now substitute g(x) into the function g(x)=3−x:
f(g(x)) = 2^(3−x)
So, the composition of f and g is f(g(x)) = 2^(3−x).
For question 1B, you need help with combining the functions f(x)=sinx and g(x)=x. To find the result of combining these functions, follow the same steps as explained above:
1. Write the composition of the two functions:
(f ∘ g)(x) = f(g(x))
2. Substitute g(x) into f(x):
f(g(x)) = sin(g(x))
3. Now substitute g(x) into the function g(x)=x:
f(g(x)) = sin(x)
Therefore, the composition of f and g is f(g(x)) = sin(x).