Find the formulas for the functions f(g(x)) and g(f(x))when f(x) = 2/x and g(x) = 2x^2-1
f(g(x)) = ?
g(f(x)) = ?
for f(g(x)) would it be 2/x(2x^2-1)
or g(f(x)) 2x^2(2/x)-1?
Would i solve like this? also when I tried to input the answer after solving didn't get the answer. Maybe i am inputting it wrong
For f(g(x)), you would input the function of g(x) for the x in f(x) to get:
2/x
2/(2x^2-1)
For g(f(x)), you would input f(x) in for the x in the function g(x):
2x^2-1
2(2/x)^2 - 1
2(4/x^2) - 1
8/x^2 - 1
proceed this way:
f(g(x))
= f(2x^2 - 1)
= 2/(2x^2 - 1)
test it for some number
e.g. let x = 3
g(3) = 18-1 = 17
f(g(3))
= f(17) = 2/17
in my answer:
2/(2x^2 - 1) = 2/17
This does not 'prove' that my answer is correct, but there is high probability that it is.
Had my answers been different, it would have "proven" that my answer was wrong.
Your answer to g(f(x)) is also incorrect.
You seem to slip in extra x's for some strange reason.
give it another try and test it with some value of x
Thanks for the help!!
To find the formulas for the functions f(g(x)) and g(f(x)), we need to substitute the equation of f(x) into g(x) and vice versa.
Let's start with f(g(x)). We substitute g(x) into f(x):
f(g(x)) = 2 / (g(x))
Now, we substitute the equation of g(x) into f(g(x)):
f(g(x)) = 2 / (2x^2 - 1)
So, the formula for f(g(x)) is 2 / (2x^2 - 1).
Now, let's find the formula for g(f(x)). We substitute f(x) into g(x):
g(f(x)) = 2(f(x))^2 - 1
Substituting the equation of f(x) into g(f(x)):
g(f(x)) = 2(2/x)^2 - 1
Simplifying this expression, we get:
g(f(x)) = 8/x^2 - 1
So, the formula for g(f(x)) is 8/x^2 - 1.
Now, when you try to input these formulas into a calculator or computer program, make sure you use parentheses correctly, as a missing or misplaced parenthesis can give inaccurate results. For f(g(x)), input it as 2 / (2x^2 - 1), and for g(f(x)), input it as 8/x^2 - 1.