find an equation for f^-1(x), the inverse function

verify that your equation is correct by showing that f(f^-1(x))=x and f^-1(f(x))=x

f(x)=x+3
f(x)=4x

Question

find an equation for f^-1(x), the inverse function

verify that your equation is correct by showing that f(f^-1(x))=x and f^-1(f(x))=x

f(x)=x+3
f(x)=4x

anonymous · Answer

$$f(x)=x+3 ==  y = x+3$$
$$y=x+3$$
$$x=y-3$$
the inverse is:
$$f(x)^{-1}=x-3$$

$$f(x)=4x$$
$$y=4x$$
$$x=y/4$$
the inverse is:
$$f(x)^{-1}=x/4$$

remember, for a function to have inverse it has to be one to one function, a one to one function must pass vertical line test, that is, a each x has unique y

anonymous · Answer

$$f(x-3)=(x-3)+3=x$$
$$f(x/4)=4(x/4)=x$$

anonymous · Answer

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