Question

Find the inverse of the following function and state its domain.

f(x)= 11cos(10x)/7
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A) f⁻¹(x) = (7/11) * cos⁻¹(10x/7), Domain: [-7/11, 7/11]
B) f⁻¹(x) = (7/11) * cos⁻¹(x/10), Domain: [-1/10, 1/10]
C) f⁻¹(x) = (7/11) * cos⁻¹(7/(10x)), Domain: (-[infinity], -7/10] ∪ [7/10, [infinity])
D) f⁻¹(x) = (7/11) * cos⁻¹(7x/10), Domain: [-10/7, 10/7]

Answer 1

The inverse function of f(x) = 11cos(10x)/7 is f⁻¹(x) = (7/110) *cos⁻¹(10x/7), and its domain is [-7/11, 7/11].

Step-by-step explanation:

The function provided is f(x) = 11cos(10x)/7. To find the inverse f⁻¹(x), we swap x and y in the equation and solve for y. This gives us:

1. x = 11*cos(10y)/7
2. 7x/11 = cos(10y)
3. cos⁻¹(7x/11) = 10y
4. y = (1/10) *cos⁻¹(7x/11)

So, f⁻¹(x) = (1/10) *cos⁻¹(7x/11) or f⁻¹(x) = (7/110) *cos⁻¹(10x/7). The domain of the inverse function is the range of the original function, which is bounded by the range of the cosine function, [-1, 1]. Considering the coefficient in front of x, the domain is adjusted to [-7/11, 7/11].