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)

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