Operations on Functions.pdf
- 2. A function is a relation that assigns to each input value exactly one output value. Like numbers and polynomials we can add, subtract, multiply and divide functions which results into a new function. Several functions can work together in one larger function. There are 5 common operations that can be performed on functions. The four basic operations on functions are adding, subtracting, multiplying, and dividing. The notation for these functions is as follows: Addition (f + g)(x) = f(x)+ g(x) Subtraction (f − g)(x)= f(x) − g(x) Multiplication (f · g)(x)= f(x) ∙ g(x) Division 𝒇 𝒈 (x) = 𝒇(𝒙) 𝒈(𝒙)
- 3. Example: Given P(x) = 4 -2x and Q(x) = 9 –x2, find (a) P(x) + Q(x) (b) P(x) - Q(x) (c) P(x)Q(x) (d) 𝑷(𝒙) 𝑸(𝒙) (a) P(x) + Q(x) = (4-2x) + (9 –x2) = 13 – 2x –x2 (b) P(x) - Q(x) = (4-2x) - (9 –x2) = x2 -2x - 5 (c) P(x)Q(x) = (4-2x) (9 –x2) = 2x3 – 4x2 – 18x +36 (d) 𝑷(𝒙) 𝑸(𝒙) = (4−2x) (9 –x2)
- 4. Your turn! Let f(x) = x + 1 and g(x) = 2x + 1, find (a) f(x) + g(x) (b) f(x) - g(x) (c) f(x)g(x) (d) 𝒇(𝒙) 𝒈(𝒙)
- 5. Example 1. f(x) = x 2 − x − 2 and g(x)= x +1 , find (f + g)( − 3)
- 6. Your turn! f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3, find (f + g) (2)
- 7. Example 2. f(x)= 2x − 4 and g(x)= x2 − x + 5, find (f – g)(4)
- 8. Your turn! f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3, find (f – g) (3)
- 9. Example 2. h(x) =2x − 4 and k(x) = − 3x + 1 Find (h · k)(5)
- 10. Your turn! g(x) = 3x + 1 and f(x) = x3 + 3x2 Find g(2)· f(2)
- 11. Example 2. h(n) = 2n − 1 and g(n) = 3n − 5 Find h(n) g(n) (0)
- 12. Your turn! f(a) = − 2a − 4 and g(a) = a2 + 3 Find ( 𝒇 𝒈 )(7)
- 13. Seatwork: by pair 1) g(a) = a3 + 5a2 and f(a) = 2a + 4. Find g(3)+ f(3) 2) d(x) = 4x + 3 and s(x) = x3 − 2x2 . Find (d−s)( − 1) 3) t(x) = 5x + 1 and r(x) = x + 3x2 . Find t(2)· r(2) 4) g(n) = n2 + 5 and f (n) = 3n + 5. Find 𝒈(𝒏) 𝒇(𝒏)
- 14. For numbers 5-8 Let f(x) = x + 2and g(x) = x2 + 1, find (a) f(x) + g(x) (b) f(x) - g(x) (c) f(x)g(x) (d) 𝒇(𝒙) 𝒈(𝒙)