f(x)=x^4 -3, g(x)=4th square root x-3, h(x)=x^4 + 3
Would the inverse be g(x) and h(x)
g(x) = 4rtroot (x-3)
x= 4rtroot (G-3)
x^4= G-3
G= x^4+3
Is h(x) the inverse of g?
what is invebrase
To determine if g(x) and h(x) are the inverses of f(x), we need to check if their composition results in the identity function.
Let's compute the composition of f(g(x)):
f(g(x)) = f(4th square root (x-3))
= (4th square root (x-3))^4 - 3
= ((x-3)^(1/4))^4 - 3
= (x-3)^(4/4) - 3
= (x-3) - 3
= x - 6
As we can see, the composition of f(g(x)) results in x - 6, which is not the identity function f(x) = x. Therefore, g(x) is not the inverse of f(x).
Now let's compute the composition of f(h(x)):
f(h(x)) = f(x^4 + 3)
= (x^4 + 3)^4 - 3
= x^16 + 3 - 3
= x^16
The composition of f(h(x)) simplifies to x^16, which is the identity function f(x) = x. Therefore, h(x) is the inverse of f(x).
In conclusion, g(x) is not the inverse of f(x), but h(x) is the inverse of f(x).