Question

An equation that defines y as a function of x is given. a. Solve for y in terms of x and

replace y with the function notation f(x). b. Find f(3).
y + 3x² = 5-3x

Answer 1

a. f(x) = - 3x² -3x + 5

b. f(3) = -31

Explanation:

y + 3x² = 5-3x

Subtract 3x² from both sides
y + 3x² - 3x² = 5 - 3x - 3x²

y = - 3x² -3x + 5 (re-arranging terms on RHS)

This the equation for y in terms of x:
f(x) = - 3x² -3x + 5

f(3) can be found by substituting x with 3 in the above equation

f(3) = -3 x 3² - 3 x 3 + 5
f(3) = -3 x 9 - 9 + 5

f(3) = -27 - 9 + 5

f(3) = -31