Function Misconceptions


ff and gg are two functions such that (fg)(3)=5(f \circ g)(3)=5

What is the value of (gf)(3)(g \circ f)(3) ?

If ff is a function with domain R\mathbb{R} and range R\mathbb{R}, does there exist a function gg such that g(x)=f1(x)g(x) = f^{-1}(x) ?

In the above image, the red graph is a graph of y=f(x)y=f(x), for some function ff.

What transformation of ff will produce the blue graph in the above graph?

f(x)f(x) is a function with domain R.\mathbb{R}.

g(x)g(x) is a horizontal transformation of f(x)f(x) such that g(x)=f(x+k).g(x) = f(x+k).

h(x)h(x) is a vertical transformation of f(x)f(x) such that h(x)=f(x)+k.h(x) = f(x)+k.

If you choose f(x)f(x) carefully, is it possible that g(x)g(x) might equal h(x)h(x) for all xx?

ff is a function whose domain is R\mathbb{R}.

gg is a function such that g(x)=f1(x)g(x)=f^{-1}(x)

True or false: The domain of gg must also be R\mathbb{R}.


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