Find f(g(x)) and g(f(x)). State the domain and formula for each.
f(x)=7x+8; g(x)=x-3
Thank you!!
To find the composition f(g(x)), we substitute the function g(x) into f(x).
f(g(x)) = 7(g(x)) + 8
Replacing g(x) with its formula:
f(g(x)) = 7(x - 3) + 8
Expanding and simplifying:
f(g(x)) = 7x - 21 + 8
f(g(x)) = 7x - 13
Therefore, the formula for f(g(x)) is 7x - 13.
Next, let's find g(f(x)) by substituting the function f(x) into g(x).
g(f(x)) = f(x) - 3
Replacing f(x) with its formula:
g(f(x)) = 7x + 8 - 3
Simplifying:
g(f(x)) = 7x + 5
Hence, the formula for g(f(x)) is 7x + 5.
Now, let's determine the domain for each function:
For f(x) = 7x + 8, there are no restrictions on the input x, so the domain is all real numbers.
For g(x) = x - 3, there are also no restrictions on the input x, so the domain is also all real numbers.
In summary:
f(g(x)) = 7x - 13, with a domain of all real numbers.
g(f(x)) = 7x + 5, with a domain of all real numbers.
f(g) = 7g+8 = 7(x-3)+8 = 7x-13
do g(f) in like wise
the domain of any polynomial is all reals.