Question

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

Answer 1

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

Answer 2

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

Answer 3

Thanks for the help!!