h(x)= x/(x-2) and g(x)= 2/x. Find and simplify
h of g(x).
I plugged g(x) into h:
h(x)= (2/x)/[(2/x)-2]
Now, would I multiply each by x, the Common Denominator?
Therefore getting 2/(2-2x) which simplifies to 1-x?
2/(2-2x) is correct, but when simplified gives 1/(1-x).
Ah, that was a stupid mistake on my part. I blame the late hour...
Thank you for your help, have a good night!=)
You're welcome! Get some sleep!
To find h(g(x)), you plug g(x) (which is 2/x) into the function h(x) and simplify. Here's how you do it:
Start with the function h(x) = x/(x-2).
Replace x in h(x) with g(x):
h(g(x)) = (2/x) / ((2/x) - 2)
Simplify the expression inside the denominator:
h(g(x)) = (2/x) / (2/x - 2) = (2/x) / ((2 - 2x)/x)
To divide by a fraction, you can multiply by its reciprocal:
h(g(x)) = (2/x) * (x/(2 - 2x))
Cancel out the x terms in the numerator and denominator:
h(g(x)) = 2 / (2 - 2x)
The expression 2 / (2 - 2x) is already simplified, and it is not equivalent to 1 - x. It's important to be careful with the simplification process.