et f(x)=5 x − 4 and g(x) = x2 − 8. Compute the following functions.
1. f(g(x)) =
2. g(f(x)) =
3. f(f(x)) =
4. g(g(x)) =
so you now f (x)= 5x - 4 so now for the 1st one plug in g(x) into the 5X
f(g(x))= 5(x2-8)-4
f(g(x))= 5x2-40-4
f(g(x))= 5x2-44
do the same for the others
let f(x)=5 x − 4 and g(x) = x^2 − 8. Compute the following functions.
1. f(g(x)) =
2. g(f(x)) =
3. f(f(x)) =
4. g(g(x)) =
To compute the following functions, we need to substitute the given expressions of f(x) and g(x) into each function.
1. f(g(x)):
Substitute g(x) into f(x):
f(g(x)) = 5(g(x)) - 4
= 5(x^2 - 8) - 4
= 5x^2 - 40 - 4
= 5x^2 - 44
Therefore, f(g(x)) = 5x^2 - 44.
2. g(f(x)):
Substitute f(x) into g(x):
g(f(x)) = (f(x))^2 - 8
= (5x - 4)^2 - 8
= (5x - 4)(5x - 4) - 8
= 25x^2 - 20x - 20x + 16 - 8
= 25x^2 - 40x + 8
Therefore, g(f(x)) = 25x^2 - 40x + 8.
3. f(f(x)):
Substitute f(x) into itself:
f(f(x)) = f(5x - 4)
= 5(5x - 4) - 4
= 25x - 20 - 4
= 25x - 24
Therefore, f(f(x)) = 25x - 24.
4. g(g(x)):
Substitute g(x) into itself:
g(g(x)) = (g(x))^2 - 8
= (x^2 - 8)^2 - 8
= (x^2 - 8)(x^2 - 8) - 8
= x^4 - 8x^2 - 8x^2 + 64 - 8
= x^4 - 16x^2 + 56
Therefore, g(g(x)) = x^4 - 16x^2 + 56.