Topic: Evaluating Functions

Please explain it (not just plain solution but statement of the process). I want to understand it clearly step by step, I hope you can help me. See the example. Clear handwriting please.

Example 1: Evaluate the following functions at x = 2. 1. f (xx) = 5x + 3 Answer: f (x) = 5(2) + 3 = 10 + 3 = 13 2. r (x) = 3x2 - 2x + 1 Answer: r (x) = 3(2)2 - 2(2) + 1 = 12-4+ 1=9 3. h (x) = vx+2 Answer: h()) = v2 +2 = v4 = 2 4. m (x) = 2x+3 x-1 Answer: m(x = 2 (2)+3 . = 7 2-1 Example 2: Fir d h(-6) and m(1) where h and m are as defined in the previous example. Answer. This is not possible. When x is replaced by -6, the resulting number is -4 and square root of a negative number is not a real number. So, -6 is not in the domain of h (x). m(1) is not defined since denominator becomes 0. So, 1 is not in the domain of the function. Example 3: Evaluate the following functions, where fand r are as defined in Example 1. a. f (2x + 1) b. r(3x - 2) Answer: a. Substitute (2x + 1) to the variable x in f (x) = 5x + 3. So, (2x + 1)- 5(2x + : )+ 3 * 10x+5+3 f(2x + 1) = 10x + 8. b. Substitute (3x - 2) to the variable x in r(x) = 3x2 - 2x + 1. So, r(3x - 2) = 3(3x - 2)'- 2(3x - 2) + 1 - 3(9x - 12x + 4) - 6x + 4 + 1 = 27x2 - 36x + 12 - Gx + 4+1 r(3x - 2) = 27x2 - 42x + 17.TASK 1. Evaluate the functions with the given values from the domain. A. fix) - 2x- - 2x + ] 1. x= 2 2. x - a 3. x = - a 4. x = a+b B. f(x) = x* + 2x] - x2+ 3x + :: 5. x = 2 6. x = 1 7. x= 0 8. X =-2 C. f(x) = 5x2 + 2x - 2 9. (10) 10. f(x+ 1) TASK 2. Evaluate the following functions at x 44. 1. f (x) = x+4 2. g (x) = x + 3x - 2 3. h(x) = vx2 -x+3 4. p (x) = V x+4 5. r (x) - +1 X-2 6. For what values of x can we not evaluate the function f(x)- TASK 3. Evaluate the given piecewise function. x-5, ifx 7 Find: a. f(-2) b. f(0) c. ((10) 2. A mobile plan costs ?400 a month. The plan includes 450 free minutes of calls and charges P5 for an additional minute of usage. The monthly charges according to the number of minutes used is given by (400, if OSX S 450 400 + 5(x - 450). if x > 450. Find the total charges for a. 150 minutes b. 450 minutes c. 560 minutes