Question 2: Evaluate the following functions for the indicated independent variables:

Solution

(a). f(x) = 3x² + 7x – 5; f(3), f(-4), f(a+h)

The given function is f(x) = 3x² + 7x – 5
Therefore, for x = 3
f(3) = 3 × 3² +7×3 – 5
f(3) = 3 × 9 + 21 – 5
f(3) = 27 + 21 – 5
f(3) = 43

The given function is f(x) = 3x² + 7x – 5
Therefore, for x = -4
f(-4) = 3 (-4)² + 7(-4) – 5
f(-4) = 3 × 16 – 28 – 5
f(-4) = 48 – 28 – 5 = 48 – 33
⇒ f(-4) = 15

The given function is f(x) = 3x² + 7x – 5
Therefore, put x = a + h
f(a + h) = 3(a + h)² + 7(a + h) – 5
f(a + h) = 3(a² + h² + 2ah) + 7a + 7h – 5
f(a + h) = 3a² + 3h² + 3×2ah +7a +7h – 5
f(a + h) = 3a² + 3h² + 6ah + 7a +7h – 5

(b). f(t) = (t+5)/(t-3); f(2), f(7.4), f(-3.7)