Let f(x)=(4x^3+20)^2 and g(x)= 4x^3+20. given that f(x)=(h o g)(x), find h(x)
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We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is . The graph of the function does not show a phase shift. We are asked to write the equation of our function.
We know that general form a cosine function is , where,
A = Amplitude,
= Period,
c = Horizontal shift,
d = Vertical shift.
The equation of parent cosine function is . Since function is reflected about x-axis, so our function will be
.
Let us find the value of b.
Upon substituting our given values in general cosine function, we will get:
Therefore, our required function would be .