Let h(x) = 3 x2 + 2 x + 1.
Let g(x) = 3√{x} + 3.
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Find the following:
(a) g(h(x)) =
(b) h(g(x)) =
(c) h(h(x)) =
(d) g(x) + 1 =
(e) g(x+1) =
ummm how old r u?
To find the values of g(h(x)), h(g(x)), h(h(x)), g(x) + 1, and g(x+1), we need to substitute the given functions into each other.
(a) g(h(x)):
To find g(h(x)), we substitute h(x) into the function g(x):
g(h(x)) = 3√(h(x)) + 3
Now we substitute h(x) into the equation:
g(h(x)) = 3√(3x^2 + 2x + 1) + 3
(b) h(g(x)):
Similarly, to find h(g(x)), we substitute g(x) into the function h(x):
h(g(x)) = 3(g(x))^2 + 2(g(x)) + 1
Now we substitute g(x) into the equation:
h(g(x)) = 3(3√(x) + 3)^2 + 2(3√(x) + 3) + 1
(c) h(h(x)):
To find h(h(x)), we substitute h(x) into the function h(x):
h(h(x)) = 3(h(x))^2 + 2(h(x)) + 1
Now we substitute h(x) into the equation:
h(h(x)) = 3(3x^2 + 2x + 1)^2 + 2(3x^2 + 2x + 1) + 1
(d) g(x) + 1:
To find g(x) + 1, we simply add 1 to the function g(x):
g(x) + 1 = 3√(x) + 3 + 1
Simplifying the equation:
g(x) + 1 = 3√(x) + 4
(e) g(x+1):
To find g(x+1), we substitute (x+1) into the function g(x):
g(x+1) = 3√(x+1) + 3
These are the expressions for g(h(x)), h(g(x)), h(h(x)), g(x) + 1, and g(x+1) based on the given functions h(x) and g(x).