Question

Find two functions which satisfy the condition fog=gof

Answer 1

Step-by-step explanation:

fog (x)= gof (x)

This can also be written as

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

This means both the functions are inverse of each other e.g. even if we reverse the order, we get the same answer. For instance

F(x) = x^5

G(x) = x^1/5  

Now, lets solve it

Fog = (x^1/5)^5 = 5

Gof = (x^5)^1/5 = 5

Hence, proved that fog = gof

Answer 2

(1) f(x) = xⁿ and g(x) = x^(1/n)

(2) f(x) = x + 2 and g(x) = x - 2

Step-by-step explanation:

(1) If we take

$f(x)=x^n$

$g(x)=\sqrt[n]{x}$

Then

$fog=f(g(x))=f(\sqrt[n]{x})=(\sqrt[n]{x})^n=(x^{1/n})^n=x$

$gof=g(f(x))=g(x^n)=\sqrt[n]{x^n}=(x^{n})^{1/n}=x$

Therefore,

$fog=gof$

(2) If we take

$f(x)=x+2$

$g(x)=x-2$

Then

$fog=f(g(x))=f(x-2)=(x-2)+2=x$

$gof=g(f(x))=g(x+2)=(x+2)-2=x$

Therefore,

$fog=gof$

Hope this answer is helpful.

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