Which of these pairs of functions are inverse functions please help :(
1 answer:
Answer:
see below (both 2nd and 3rd choices)
Step-by-step explanation:
One way to tell if the functions are inverses is to look at f(g(x)). If the functions are inverses, then f(g(x)) = x.
A: f(g(x)) = 2^((log2(x -1) -1) -1) +1 = (2^(log2(x-1))(2^-2) +1 = (1/4)(x -1) +1 ≠ x
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B: f(g(x)) = (1/2)(ln((2e^(2x+1))/2) -1) = (1/2)(ln(e^(2x+1)) -1) = (1/2)(2x +1 -1) = x
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C: f(g(x)) = 4ln(e^((e^2x/8))^2)/e^2 = 8(e^2x/8)/e^2 = x
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D: f(g(x)) = 10^((log(x+10)-10) -10)-10 = (10^log(x+10))(10^-10) -10
= (x +10)(10^-10) -10 ≠ x
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The 2nd and 3rd pairs of functions listed are inverses of each other.
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Answer: 3 zeroes.
Explanation:-
- The fundamental theorem of algebra states that any polynomial with degree m>0 and complex coefficients has atleast one complex root.
- Corollary of fundamental theorem states that for any polynomial with degree m>0 has exactly m solutions.
The given function is
Because it is a polynomial function with degree 3>0 , Therefore by corollary of fundamental theorem of algebra , it has 3 zeroes.