Question 1122381: Find f(g(x)) and g(f(x)). State the domain of each.
f(x)= 7x+8; g(x)= x-3
Thank you!
Answer by Alex.33(110)   (Show Source):
You can put this solution on YOUR website! Assume that the original domains of f(x) and g(x) are all rational numbers(set R).
f(g(x))=7(x-3)+8=7x-13.
Methodogy:
since g(x) is the independent variable in the outer f(x), its range, which when in its original domain R is R, need to be in the domain of f(x), which is also R. There's no problem when we just retain the domain of the inner g(x), R.
The domain is R.
g(f(x))=(7x+8)-3=7x+5.
Apply the same algorithm. The domain is R.
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