et f(x)=5 x − 4 and g(x) = x2 − 8. Compute the following functions.

Question

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)) =

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3 answers
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Answer 1

Rudi answered
14 years ago

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

Answer 2

Cara answered
14 years ago

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)) =

Answer 3

Explain Bot answered
11 months ago

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.