Asked by T.
Determine whether f(x)=5x+1/x and g(x)= x/5x+1 are inverse functions. Explain how you know.
Help please?
Help please?
Answers
Answered by
oobleck
if f and g are inverses, then f(g(x) = g(f(x)) = x
I'll check f(g). You can do g(f)
Hmmm. I assume you meant
f(x) = (5x+1)/x and g(x) = x/(5x+1)
If so, it is immediately clear that g(x) = 1/f(x), not f<sup><sup>-1</sup></sup>(x). They are reciprocals, not inverses.
But, who knows? Maybe they are also inverses.
f(g) = (5g+1)/g = (5*x/(5x+1) + 1)/(x/(5x+1))
= (5x+5x+1)/x = (10x+1)/x = 10 + 1/x ≠ x
In fact, f<sup><sup>-1</sup></sup>(x) = 1/(x-5)
If we use f and g as you typed them, the situation is even worse, but they are clearly not inverses.
I'll check f(g). You can do g(f)
Hmmm. I assume you meant
f(x) = (5x+1)/x and g(x) = x/(5x+1)
If so, it is immediately clear that g(x) = 1/f(x), not f<sup><sup>-1</sup></sup>(x). They are reciprocals, not inverses.
But, who knows? Maybe they are also inverses.
f(g) = (5g+1)/g = (5*x/(5x+1) + 1)/(x/(5x+1))
= (5x+5x+1)/x = (10x+1)/x = 10 + 1/x ≠ x
In fact, f<sup><sup>-1</sup></sup>(x) = 1/(x-5)
If we use f and g as you typed them, the situation is even worse, but they are clearly not inverses.
Answered by
peter wagih
Verify that f(x)=5x-1 and g(x)=(x+1)/5 are inverse functions
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