Part A Consider functions m and n: n(x)=1/4x^2-2x+4
The value of m(n(2)) is __
The value of n(m(1)) is __

Part B
Consider the functions m and n
n(x)=1/4x^2-2x+4
What is the value of n(m(4))
A. -4
B. -2
C. 0
D. 4

Part C
Given your answers to Katy’s A and B, do you think functions m and n are inverse functions? Explain your reasoning.

Part A

The value of m(n(2)) is 2.

The value of n(m(1)) is 1.

Part B

The value of n(m(4)) is 0.

Part C

To be inverse functions, the values of n(m(x)) and m(n(x)) must equal x for all values of x in the domain. In part A, there were two cases where the value of the composite function was equal to x. In part B, however, there was a case where n(m(x)) was not equal to x. Therefore, the two functions cannot be inverse functions.

Step-by-step explanation:

PLATO

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47