f(x)=1x, g(x)=1x, then (f∘g)(x)
1x is the same as x
(f∘g)(x)
= f(g(x) )
= f(x)
= x
so is g of x the inverse
did you mean f(x) and g(x) to be the same and = x ??
in that case y = x is the equation for both
and the inverse of y = x is indeed y = x
f(x)=x2−1, g(x)=2x+2, then (fg)(x)=
x2−12x+2, x≠1
so is this correct
cuz i got x ≠ -1
I assume we are doing a new question and
f(x) = x^2 - 1 , g(x) = 2x + 2
then
(fg)(x)
= f(g(x))
= f(2x + 2)
= (2x + 2)^2 - 1
= 4x^2 + 8x + 4 - 1
= 4x^2 + 8x + 3
test with some value, say x = 3
g(x) = 2(3) + 2 = 8
f(x) = x^2 - 1
f(8) = 64 - 1 = 63
f(g(3)) = 4(9) + 8(3) + 3
= 63
It is highly probable that my answer is correct
To find the composition function (f∘g)(x), we need to substitute the function g(x) into the function f(x).
Given that f(x) = 1x and g(x) = 1x, we can substitute g(x) into f(x) as follows:
(f∘g)(x) = f(g(x))
Substituting g(x) into f(x), we have:
(f∘g)(x) = f(1x)
Now, we substitute 1x into f(x) by replacing each occurrence of x in f(x) with 1x:
(f∘g)(x) = 1(1x)
Simplifying the expression, we have:
(f∘g)(x) = 1 * 1x
Finally, we can simplify this to:
(f∘g)(x) = 1x
Therefore, the composition function (f∘g)(x) is equal to 1x.