EVALUATE PIECEWISE FUNCTION QUESTIONS AND ANSWERS

Evaluate Piecewise Function Questions with Answers :

Here we are going to see, how to evaluate piecewise functions.

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.

Evaluate Piecewise Function Questions with Answers - Questions

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 + 2f(2)  =  2 + 2  =  4 f(x)  =  x - 1f(-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) + 1f(-3)  =  -17 f(2)  = 5(2)2 - 1f(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 - 4f(7)  =  17 f(1)  =  6(1) + 1  =  6 + 1f(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 - 1f(4)  =  79 f(8)  =  3x - 4  =  3(8) - 4f(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) + 1f(-2)  =  -11f(4)  =  79 f(6) = 3(6) - 4   =  18 - 4f(6)  =  14

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

=  (-22 - 14) / (79 - 11)

=  -36/68

=  -9/17

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