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Answer:
a. 7
b. -18
c. 5
d. 8
e. 5a + 2
f. a² + 4a + 8
Step-by-step explanation:
f(x) = 5x - 3 and g(x) = x² + 2x + 5
for each, we simply plug in what's inside of the parenthesis wherever we see x
f(2) = 5(2) - 3
multiply 5 and 2
f(2) = 10 - 3 = 7
f(-3) = 5(-3) - 3
multiply 5 and -3
f(-3) = -15 - 3 = -18
g(-2) = (-2)² + 2(-2) + 5
evaluate exponent
g(-2) = 4 + 2(-2) + 5
multiply 2 and -2
g(-2) = 4 - 4 + 5 = 5
( the 4's cancel out and we're left with 5 )
g(1) = (1)² + 2(1) + 5
evaluate exponent
g(1) = 1 + 2(1) + 5
multiply 2 and 1
g(1) = 1 + 2 + 5 = 8
f(a+1) = 5(a + 1) - 3
distribute the 5
f(a+1) = 5a + 5 - 3
combine like terms
f(a+1) = 5a + 2
g(a+1) = (a+1)² + 2(a+1) + 5
expand exponent
g(a+1) = (a+1)(a+1) + 2(a+1) + 5
evaluate (a+1)(a+1) using FOIL
g(a+1) = a² + 2a + 1 + 2(a+1) + 5
distribute the 2
g(a+1) = a² + 2a + 1 + 2a + 2 + 5
combine like terms
g(a+1) = a² + 4a + 8