Two functions g and h are defined as :
g:x--> 2x+3/x-4
h:x --> 1/x
Write expressions for :
a) hg(x)
To find the expression for hg(x), we need to substitute the function h into the function g.
The function h(x) is given as h:x --> 1/x.
Now, let's substitute h(x) into g(x):
hg(x) = g(h(x))
Replacing h(x) in g(x) with its expression, we get:
hg(x) = g(1/x)
Now let's substitute the expression of g(x) into this equation:
hg(x) = (2(1/x) + 3)/(1/x - 4)
Simplifying this expression further, we can multiply the numerator and the denominator by x to remove the fractions in the equations:
hg(x) = (2/x + 3x)/(1 - 4x)
So, the expression for hg(x) is (2/x + 3x)/(1 - 4x).