Question

Given f(x) = x - 2 and g(x) = 5x +3, evaluate each function and match the correct answer.ITEM BANK Move to Topg(2x))drag and drop answer here-14RR1))drag and drop answer here-22919(-1))drag and drop answer here-3-7g(1-3))drag and drop answer here55-7fig(-3))drag and drop answer here

Answer 1

The given functions are

f(x) = x - 2

g(x) = 5x + 3

1) To find g(f(x)), we would substitute f(x) into g(x). Thus,

g(f(x)) = 5(x - 2) + 3 = 5x - 10 + 3

g(f(x)) = 5x - 7

2)To find f(f(1)), we would substitute f(x) into f(x) to get f(f(x)) and substitute x = 1 into the f(f(x)). Thus, we have

f(f(x)) = (x - 2) - 2 = x - 2 - 2 = x - 4

f(f(1)) = 1 - 4

f(f(1)) = - 3

3) g(g(x)) = 5(5x + 3) + 3 = 25x + 15 + 3 = 25x + 18

g(g(-1)) = 25(-1) + 18 = - 25 + 18

g(g(-1)) = -7

4) g(f(x)) = 5(x - 2) + 3 = 5x - 10 + 3 = 5x - 7

g(f(-3)) = 5(-3) - 7 = - 15 - 7

g(f(-3)) = - 22

f(g(x)) = 5x + 3 - 2 = 5x + 1

f(g(-3)) = 5(-3) + 1 = - 8 + 1

f(g(-3)) = - 7