For which pairs of functions is ?
Asked by maham237 @ in Mathematics viewed by 291 People
For which pairs of functions is f(g(x))=x?
A) f(x)=x^2 and g(x)=1/x
B) f(x)=2/x and g(x)=2/x
C) f(x)x-2/3 and g(x)=2-3x
D) f(x)1/2x-2 and g(x)=1/2x+2
Asked by maham237 @ in Mathematics viewed by 291 People
For which pairs of functions is f(g(x))=x?
A) f(x)=x^2 and g(x)=1/x
B) f(x)=2/x and g(x)=2/x
C) f(x)x-2/3 and g(x)=2-3x
D) f(x)1/2x-2 and g(x)=1/2x+2
Answered by maham237 @
The right answer is B) f(x)=2/x and g(x)=2/x
This is a problem of composition of functions.
So, the only functions that satisfies this concept is B). To prove this, let's take the following steps:
Since this composition of functions gives us the identity function, then we can conclude that the function g is the inverse of f and vice versa.
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