1.Let f(x)= x^2 - 5 and g(x)= 3x^2. Find g(f(x)).
2. Let f(x)= x^2 - 4 and g(x) -3x^2. Find f(g(x)).
g(x)= -3x^2
g(f(x))= -3(x^2-4)^2
-6(x^2-4)(2x)
-6x^2-24 (2x)
-12x^3-48x
-12x(x^2+4)
f(g(x))= (-3x^2)^2-4
2(-3x^2)(-6x)-4
-6x^2(-6x)-4
36x^3-4
4(9x^3-1)
I think you're doing it wrong, because I am not getting those answers. I got answer choices.
Neil -- for heaven's sakes! If you have answer choices, please post them along with your problem!
1. Let f(x)= x^2 - 5 and g(x)= 3x^2. Find g(f(x)).
A. 3x^4 - 30x^2 + 75
B. -3x^4 - 15
C. 9x^4
D. -3x^4 - 4
2. Let f(x)= x^2 - 4 and g(x)= -3x^2. Find f(g(x)).
F. -3x^4 + 12
G. -3x^4 + 24x^2 - 48
H. 9x^4 - 4
I. -3x^4 - 4
To find g(f(x)), we need to substitute f(x) into the function g(x).
1. Start with the given functions:
f(x) = x^2 - 5
g(x) = 3x^2
2. Substitute f(x) into g(x):
g(f(x)) = 3(f(x))^2
3. Substitute the value of f(x) into g(f(x)):
g(f(x)) = 3(x^2 - 5)^2
4. Simplify the expression by expanding the square:
g(f(x)) = 3(x^4 - 10x^2 + 25)
Therefore, g(f(x)) = 3x^4 - 30x^2 + 75.
To find f(g(x)), we need to substitute g(x) into the function f(x).
1. Start with the given functions:
f(x) = x^2 - 4
g(x) = -3x^2
2. Substitute g(x) into f(x):
f(g(x)) = (g(x))^2 - 4
3. Substitute the value of g(x) into f(g(x)):
f(g(x)) = (-3x^2)^2 - 4
4. Simplify the expression by squaring the value inside the parentheses:
f(g(x)) = 9x^4 - 4
Therefore, f(g(x)) = 9x^4 - 4.