EVALUATE PIECEWISE FUNCTION QUESTIONS AND ANSWERS

To evaluate the given piecewise function, we need to follow the steps given below. 

(i)  Draw number line and write the values of x, according to the given interval. 

(ii) Write the appropriate function below the corresponding interval.

(iii)  Now we have to choose the function based on the value of x we find in f(x) and evaluate.

Question 1 :

If the function f is defined by

find the values of

(i) f (3) (ii) f (0) (iii) f (−1.5) (iv) f (2)+ f (−2)

Solution :

(i)  f(3)

Instead of x, we have 3. So we have to choose the function f(x)  =  x + 2

f(3)  =  3 + 2

f(3)  =  5

(ii)  f(0)

0 lies between -1 and 1. So, the answer is 2.

(iii) f (−1.5)

f(x)  =  x - 1

f(-1.5)  =  -1.5 - 1

f(-1.5)  =  -2.5

 (iv) f (2)+ f (−2)

f(x)  =  x + 2

f(2)  =  2 + 2

  =  4

f(x)  =  x - 1

f(-2)  =  -2 - 1

  =  -3

f (2) + f (−2)  =  4 + (-3)  =  1

Question 2 :

A function f : [−5,9] -> R is defined as follows:

Find (i) f (−3) + f (2) (ii) f (7) - f (1) (iii) 2f (4) + f (8)

(iv)  [2f(-2) - f(6)] / [f(4) + f(-2)]

Solution :

(i) f (−3) + f(2)

f(x)  =  6x + 1 for f(-3) and f(x)  =  5x2 - 1 for f(2)

f(-3)  =  6(-3) + 1

f(-3)  =  -17

f(2)  = 5(2)2 - 1

f(2)  =  19

f (−3) + f(2)  =  -17 + 19

f (−3) + f(2)  =  2

(ii) f (7) - f (1)

f(x)  =  3x - 4 for f(7) and f(x)  =  6x + 1  for f(1)

f(7)  =  3(7) - 4

  =  21 - 4

f(7)  =  17

f(1)  =  6(1) + 1

  =  6 + 1

f(1)  =  7

f (7) - f (1)  =  17 - 7  =  10

(iii) 2f (4) + f (8)

f(x)  =  5x2 - 1 for f(4)  and f(x)  =  3x - 4 for f(8)

f(4)  =  5(4)2 - 1

  =  80 - 1

f(4)  =  79

f(8)  =  3x - 4

  =  3(8) - 4

f(8)  =  20

 2f (4) + f (8)  =  2(79) + 20 

  =  158 + 20

  2f (4) + f (8)  =  178

(iv)  [2f(-2) - f(6)] / [f(4) + f(-2)]

f(x)  =  6x + 1 for f(-2) and f(x) = 3x - 4 for f(6)

f(-2)  =  6(-2) + 1

f(-2)  =  -11

f(4)  =  79

f(6) = 3(6) - 4 

  =  18 - 4

f(6)  =  14

 [2f(-2) - f(6)] / [f(4) + f(-2)]  =  [2(-11) - 14] / [79 + (-11)]

  =  (-22 - 14) / (79 - 11)

  =  -36/68

  =  -9/17

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Digital SAT Math : Factoring with Difference of Two Squares

    Sep 03, 25 12:30 PM

    Digital SAT Math : How to factor and simplify expressions using difference of two squares

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 271)

    Aug 31, 25 07:25 AM

    Digital SAT Math Problems and Solutions (Part - 271)

    Read More

  3. Digital SAT Math Problems and Solutions (part - 270)

    Aug 30, 25 04:19 AM

    digitalsatmath378.png
    Digital SAT Math Problems and Solutions (part - 270)

    Read More