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7. Two functions are defined below.

F(x) = 5x + 1
g(x) = x/5 - 1/5
Which presentation best establishes that the functions are inverse functions?

7. Two functions are defined below. F(x) = 5x + 1 g(x) = x/5 - 1/5 Which presentation-example-1
User Rollerball
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1 Answer

5 votes

Given:

The two functions are


f(x)=5x+1


g(x)=(x)/(5)-(1)/(5)

To find:

The presentation which establishes that the functions are inverse functions.

Solution:

Two functions f(x) and g(x) are inverse of each other, if


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

We have,


f(x)=5x+1


g(x)=(x)/(5)-(1)/(5)

Now,


g(f(x))=(5x+1)/(5)-(1)/(5)


g(f(x))=(5x)/(5)+(1)/(5)-(1)/(5)


g(f(x))=x

Similarly,


f(g(x))=5\left((x)/(5)-(1)/(5)\right)+1


f(g(x))=x-1+1


f(g(x))=x

Since,
f(g(x))=g(f(x))=x, therefore, the given functions are inverse of each other.

Hence, the correct option is C.

User Viktor Livakivskyi
by
8.5k points

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