Function fog?

Consider the function f(x) = x/1 + x , g(x) = sin(4x)

For fog(x)=sin(4x)/1+sin(4x)

State the domain of the function. (Let n represent an arbitrary integer.)

For fof(x)=x/1+2x State the domain of the function. (Enter your answer using interval notation.)

Find the function

g o g

1 Answer

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  • 2 months ago

    Assuming you mean f(x) = x/(1 + x) so (fog)(x) = sin(4x)/(1 + sin(4x)),

    The domain is all real numbers except those that lead to the denominator equaling 0.

    The domain is all real numbers except x such that

    1 + sin(4x) = 0

    sin(4x) = -1

    4x = 3pi/2 + 2npi for all integers, n

    x = 3pi/8 + npi/2 for all integers, n

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