consider the function h as defined. find functions f and g so that (f ° g)(x)=h(x).
h(x)=1 / x² - 6
the answer is f(x) = 1/x, g(x)=x² - 6
can some one plz explain to me how we got this answer
thanks....
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(f ° g)(x)=h(x).
(f ° g)(x) means f ( g(x) )
h(x)= 1/(x²-6)= f(g(x) )=
hence this can mean that f(x)=1/x
& g(x)= x²-6
so f(g(x) )= 1/(g(x)= 1/(x²-6)
hence ur ans is correct.
f(x)=1/x
g(x)=x^2-6
f (g(x)) = 1/ g(x) (can you see that if f(x) = 1/x, then f(g(x)) = 1/ g(x) ?
=1/ (x^2-6) [ you just replaced g(x) by its value]