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dallisjuhnke
11.04.2021 •
Mathematics
For f(x) = 5x – 3 and g(x) = 2x2 - 5, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2)
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Ответ:
See answer below
Step-by-step explanation:
Given the functions f(x) = 5x – 3 and g(x) = 2x2 - 5, find the following functions.
a)(fog)(x) = f(g(x))
f(g(x)) = f(2x^2-5)
f(g(x)) = 5(2x^2-5) - 3
f(g(x)) = 10x²-25-3
f(g(x)) = 10x² - 28
b) g(f(x)) = g(5x-3)
g(f(x)) = 2(5x-3)²-5
g(f(x)) = 2(25x²-30x+9)-5
g(f(x)) = 50x²-60x+18-5
g(f(x)) = 50x²-60x+13
c)(fog)(2) = f(g(2))
f(g(x)) = f(2x^2-5)
f(g(2)) = 10(2)² - 28
f(g(2)) = 10(4)-28
f(g(2)) = 12
d) g(f(x)) = g(5x-3)
g(f(x)) = 2(5x-3)²-5
g(f(x)) = 50x²-60x+13
g(f(2)) = 50(2)²-60(2)+13
g(f(2)) = 200-120+12
g(f(2)) =80+12
g(f(2)) = 92
Ответ: