Given that
f:x -->3-x
g:x --> x+2/x-5
derive the expression for gf(x)
how to combine ?? that's wat i have problem withh ??
g(f(x))=(3-x)+2/(3-x)-5 now combine terms.
Get a common denominator, and combine. If you don't know how to do that, http://regentsprep.org/Regents/math/ALGEBRA/AV5/addsubt.htm
still don't understand how to combine this . can u show me ?
To derive the expression for gf(x), we need to find the composition of the functions f and g.
First, let's find g(f(x)).
Substitute the expression for f(x) into g(x):
g(x) = (x + 2)/(x - 5)
Replace x with f(x):
g(f(x)) = (f(x) + 2)/(f(x) - 5)
Now, find the expression for f(x):
f(x) = 3 - x
Substitute this expression into g(f(x)):
g(f(x)) = (3 - x + 2)/(3 - x - 5)
Simplify the numerator and denominator:
g(f(x)) = (5 - x)/( -2 - x)
Therefore, the expression for gf(x) is (5 - x)/( -2 - x).