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jek_recluse [69]
3 years ago
10

For each pair of functions f and g below, find f(g(x)) and g(f(x)).

Mathematics
1 answer:
natta225 [31]3 years ago
5 0

Answer:

a)  f(g(x)) = \frac{1}{2(\frac{1}{2x} )} = \frac{1}{\frac{1}{x} } } = x

    g(f(x)) = \frac{1}{2(\frac{1}{2x} )} = \frac{1}{\frac{1}{x} } } = x

    f and g are inverses

b)   f(g(x)) = x + 3 + 3 = x + 6

     g(f(x)) = x + 3 + 3 = x + 6

     f and g are not inverses

Step-by-step explanation:

a)

f(g(x)) = \frac{1}{2(\frac{1}{2x} )} = \frac{1}{\frac{1}{x} } } = x

g(f(x)) = \frac{1}{2(\frac{1}{2x} )} = \frac{1}{\frac{1}{x} } } = x

Since f(g(x)) = g(f(x)) = x, then f and g are inverses

b)

f(g(x)) = x + 3 + 3 = x + 6

g(f(x)) = x + 3 + 3 = x + 6

Since f(g(x)) = g(f(x)) ≠ x, then f and g are not inverses

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