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Pepsi [2]
2 years ago
10

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

Mathematics
1 answer:
n200080 [17]2 years ago
6 0

Given:

f(x)=\dfrac{8}{x}

g(x)=\dfrac{8}{x}

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

f(g(x))=x and g(f(x))

We have,

f(x)=\dfrac{8}{x}

g(x)=\dfrac{8}{x}

Now,

f(g(x))=f(\dfrac{8}{x})              [\because g(x)=\dfrac{8}{x}]

f(g(x))=\dfrac{8}{\dfrac{8}{x}}            [\because f(x)=\dfrac{8}{x}]

f(g(x))=8\times \dfrac{x}{8}

f(g(x))=x

Similarly,

g(f(x))=f(\dfrac{8}{x})              [\because f(x)=\dfrac{8}{x}]

g(f(x))=\dfrac{8}{\dfrac{8}{x}}            [\because g(x)=\dfrac{8}{x}]

g(f(x))=8\times \dfrac{x}{8}

g(f(x))=x

Since, f(g(x))=x and g(f(x)), therefore, f(x) and g(x) are inverse of each other.

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