Question

Find (g-x)(x).
f(x)=1/x
g(x)=x^2+2x-5

Answer 1

f(x)/ g(x) = (1/x )/ ((x+1)/(x-2))

While dividing two rational expressions, take the reciprocal of the divisor(that is f(x)) and multiply it with the divident ( that is g(x) )

==> f(x)/ g(x) = (1/x )* [(x-2)/(x+1)]

==> = [ 1 * (x-2)]/[x * (x+1)]

==> = (x-2)/( x*x - x*1)

==> f(x)/ g(x) = ( x-2)/(x^2 -x )

OR we can write, f(x)/ g(x) = (x-2)/x(x + 1)

Explanation:

In the denominator, we have x(x + 1)

The values, x = 0 and x = -1 make the denominator zero.

That means for values, x = 0, -1 the function is not defined.

So we can say that domain of f(x)/ g(x) is set of all real numbers except 0 and -1

That is Domain = R - {0, -1}

I hope this helps Apex :) .