SOLUTION: What is the funtion of fof; gog; given f(x)=3-5x and g(x)=1-3x? I understand that gof is equivocated to g(f(x)) but don't understand how to do fof & gof.

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Question 19592: What is the funtion of fof; gog; given f(x)=3-5x and g(x)=1-3x? I understand that gof is equivocated to g(f(x)) but don't understand how to do fof & gof.
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
What is the funtion of fof; gog; given f(x)=3-5x and g(x)=1-3x? I understand that gof is equivocated to g(f(x)) but don't understand how to do fof & gof.
it is same way you do.in general f(x)or f of x is a function where you have all terms represented by x in different forms say x^2 0r log x or sin xor as in your present problem 3-5x or 1-3x.when it is asked to find f(a)or f of a you are supposed to substitute a in place of x wherever it occurs like in the above examples a^2 or log a or sin a or 3-5a or 1-5a ...in the same way if we have to find f(f(x))or f of f of x,it means find f(x) first..call it y say to make you feel better..then we have to next find f(y)...that is substitute y for x wherever it is...that is substitue f(x) for x wherever it is using the value of y or f(x) for the purpose...let us illustrate
we have f(x)=3-5x=y say as i suggeted
so f(f(x))=f(y)=3-5y...but y=3-5x..so
f(f(x))=3-5(3-5x)=3-15+25x=-12+25x...
i think you can now find g(g(x)) in a similar way...